Exhibit 5.1

[LETTERHEAD OF JONES WALKER LLP]

March 28, 2019

IBERIABANK Corporation

200 W. Congress Street

Lafayette, Louisiana 70501

Ladies and Gentlemen:

We have acted as special counsel to IBERIABANK Corporation, a Louisiana corporation (the “Company”), in connection with the Registration Statement on Form S-3 (the “Registration Statement”) to be filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), relating to (i) shares of common stock of the Company (par value $1.00 per share) (the “Common Stock”); (ii) warrants to purchase Common Stock (the “Common Stock Warrants”); (iii) shares of serial preferred stock of the Company (par value $1.00 per share) (the “Preferred Stock”), which may be issued in the form of depositary shares evidenced by depositary receipts (the “Depositary Shares”); (iv) warrants to purchase Preferred Stock (the “Preferred Stock Warrants”); (v) Common Stock and Preferred Stock that may be issued upon exercise of Securities Warrants (as defined below); (vi) units consisting of any combination of Securities (as defined below) (the “Units”); (vii) rights to purchase Common Stock and Preferred Stock (the “Rights”); and (viii) such indeterminate amount of Securities as may be issued in an exchange for or upon conversion of, as the case may be, the Securities (as defined herein). The Common Stock Warrants and Preferred Stock Warrants are hereinafter referred to collectively as the “Securities Warrants,” and the Common Stock, the Preferred Stock, the Depositary Shares, the Warrants, the Rights and the Units are hereinafter referred to collectively as the “Securities.” The Company may not receive separate consideration for any Securities that are issued in exchange for, or upon conversion of, as the case may be, the Securities. The Securities may be issued and sold or delivered from time to time as set forth in the Registration Statement, any amendment thereto, the prospectus contained therein (the “Prospectus”) and supplements to the Prospectus (the “Prospectus Supplements”) and pursuant to Rule 415 under the Securities Act for an indeterminate aggregate initial offering price.

The Depositary Shares will be issued pursuant to a Deposit Agreement (each, a “Deposit Agreement”) between the Company and the depository to be named therein (the “Depository”), to be filed, if necessary, by amendment to the Registration Statement or as an exhibit to one or more Current Reports on Form 8-K of the Company and incorporated by reference therein.

The Securities Warrants will be issued under a Securities Warrant Agreement (each, a “Securities Warrant Agreement”) between the Company and a warrant agent to be named therein, to be filed, if necessary, by amendment to the Registration Statement or as an exhibit to one or more Current Reports on Form 8-K of the Company and incorporated by reference therein. Each party to a Securities Warrant Agreement other than the Company is referred to hereinafter as a “Counterparty.”

The Rights will be issued under a Rights Agent Agreement (each, a “Rights Agent Agreement”) between the Company and the rights agent to be named therein (the “Rights Agent”), to be filed, if necessary, by amendment to the Registration Statement or as an exhibit to one or more Current Reports on Form 8-K of the Company and incorporated by reference therein.

The Units will be issued pursuant to a Unit Agreement (each, a “Unit Agreement”) between the Company and a unit agent to be named therein (the “Unit Agent”), to be filed, if necessary, by amendment to the Registration Statement or as an exhibit to one or more Current Reports on Form 8-K of the Company and incorporated by reference therein.

We have examined the Registration Statement, a form of Common Stock certificate and the originals, or duplicates or certified or conformed copies, of such corporate and other records, agreements, documents and other instruments and have made such other investigations as we have deemed relevant and necessary in connection with the opinions hereinafter set forth. As to questions of fact material to this opinion, we have relied upon certificates or comparable documents of public officials and of officers and representatives of the Company.

In rendering the opinions set forth below, we have assumed the genuineness of all signatures, the legal capacity of natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as duplicates or certified or conformed copies, and the authenticity of the originals of such latter documents. We also have assumed that: (1) at the time of execution, countersignature, issuance and delivery of any Securities Warrants, the related Securities Warrant Agreement will be the valid and legally binding obligation of each Counterparty thereto; (2) at the time of execution, issuance and delivery of the Depositary Shares, the related Deposit Agreement will be the valid and legally binding obligation of the Depository; (3) at the time of execution, issuance and delivery of the Rights, the related Rights Agent Agreement will be the valid and legally binding obligation of the Rights Agent; and (4) at the time of the execution, issuance and delivery of the Units, the related Unit Agreement will be the valid and legally binding obligation of the Unit Agent. We have assumed further that at the time of execution, countersignature, issuance and delivery of any Securities Warrants, the related Securities Warrant Agreement will have been duly authorized, executed and delivered by the Company. We have assumed further that at the time of execution, issuance and delivery of any Depositary Shares, the Deposit Agreement will have been duly authorized, executed and delivered by the Company. We have assumed further that at the time of execution, issuance and delivery of any Rights, the Rights Agent Agreement will have been duly authorized, executed and delivered by the Company. We have assumed further that at the time of execution, issuance and delivery of any Units, the Unit Agreement will have been duly authorized, executed and delivered by the Company.

Based upon the foregoing, and subject to the qualifications, assumptions and limitations stated herein, we are of the opinion that:

1.    With respect to the Common Stock, assuming (a) the taking by the Board of Directors of the Company or a duly constituted and acting committee of the Board of Directors of the Company (such Board of Directors and committee being referred to herein, collectively, as the “Board”) of all necessary corporate action to authorize and approve the issuance of the

Common Stock and (b) due issuance and delivery of the shares of Common Stock, upon payment therefor in accordance with the applicable definitive purchase, underwriting or similar agreement approved by the Board, the Common Stock will be validly issued, fully paid and nonassessable.

2.    With respect to the Preferred Stock, assuming (a) the taking by the Board of all necessary corporate action to authorize and approve the issuance of the Preferred Stock, (b) due filing of Articles of Amendment with respect to the Preferred Stock, to be filed with the Louisiana Secretary of State and (c) due issuance and delivery of the shares of Preferred Stock, upon payment therefor in accordance with the applicable definitive purchase, underwriting or similar agreement approved by the Board, the Preferred Stock will be validly issued, fully paid and nonassessable.

3.    With respect to the Securities Warrants, assuming (a) the taking of all necessary corporate action by the Board to approve the execution and delivery of a related Securities Warrant Agreement and (b) the due execution, countersignature, issuance and delivery of such Securities Warrants, upon payment of the consideration for such Securities Warrants provided for in the applicable definitive purchase, underwriting or similar agreement approved by the Board and otherwise in accordance with the provisions of the applicable Securities Warrant Agreement and such agreement, such Securities Warrants will constitute valid and legally binding obligations of the Company enforceable against the Company in accordance with their terms.

4.    With respect to the Rights, assuming (a) the taking of all necessary corporate action by the Board to authorize and approve (i) the issuance and terms of the Rights, (ii) the execution and delivery of the Rights Agent Agreement with respect to the Rights, (iii) the issuance of any Common Stock upon exercise of the Rights, (iv) the issuance of any Preferred Stock upon exercise of the Rights, (b) the due filing of the Articles of Amendment with respect to any such Preferred Stock and (c) the due execution, issuance and delivery of (i) the Rights, (ii) any such Common Stock or (iii) any such Preferred Stock, in each case upon the payment of the consideration therefor provided for in the applicable definitive purchase, underwriting or similar agreement approved by the Board, and in accordance with the provisions of the applicable Rights Agent Agreement, such Rights will constitute valid and legally binding obligations of the Company, enforceable against the Company in accordance with their terms. With respect to the Depositary Shares, assuming (a) the taking of all necessary corporate action by the Board to authorize and approve the issuance of the shares of Preferred Stock represented by such Depositary Shares, and the execution and delivery of the Deposit Agreement, (b) the due issuance and delivery to the Depository of the shares of Preferred Stock represented by the Depositary Shares and (c) the due execution, issuance and delivery of depositary receipts evidencing the Depositary Shares against deposit of the shares of Preferred Stock in accordance with the Deposit Agreement, upon payment of the consideration for such Depositary Shares provided for in the applicable definitive purchase, underwriting or similar agreement approved by the Company and otherwise in accordance with the provisions of the Deposit Agreement and such agreement, depositary receipts evidencing the Depositary Shares will constitute valid and legally binding obligations of the Company enforceable against the Company in accordance with their terms and will entitle the holders thereof to the rights specified in the Depositary Shares and the Deposit Agreement.

5.    With respect to the Units, assuming (a) the taking of all necessary corporate action by the Board to authorize and approve (i) the issuance and terms of the Units, (ii) the execution and delivery of the Unit Agreement with respect to the Units, (iii) the issuance of shares of any Common Stock that is a component of the Units, (iv) the issuance of shares of any Preferred Stock that is a component of the Units, (v) the execution and delivery of the Securities Warrant Agreement with respect to any Securities Warrants that are a component of the Units, (vi) the execution and delivery of the Deposit Agreement with respect to any Depositary Shares that are a component of the Units, (b) the due filing of the Articles of Amendment with respect to any such Preferred Stock and (c) the due execution, countersignature (in the case of any such Securities Warrants), issuance and delivery of (i) the Units, (ii) any such Common Stock, (iii) any such Preferred Stock, (iv) any such Securities Warrants and (v) the depositary receipts evidencing any such Depositary Shares, in each case upon the payment of the consideration therefore provided for in the applicable definitive purchase, underwriting or similar agreement approved by the Board, the applicable Securities Warrant Agreement, in the case of such Securities Warrants, and the applicable Depositary Agreement, in the case of such Depositary Shares, and in accordance with the provisions of the applicable Unit Agreement, such Units will constitute valid and legally binding obligations of the Company, enforceable against the Company in accordance with their terms.

Our opinions above are subject, as applicable, to the effects of (i) bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws relating to or affecting creditors’ rights generally, (ii) general equitable principles (whether considered in a proceeding in equity or at law), and (iii) an implied covenant of good faith and fair dealing.

We do not express any opinion herein concerning any law other than the law of the State of Louisiana and the federal law of the United States (including the statutory provisions, all applicable provisions of the Louisiana Constitution and reported judicial decisions interpreting the foregoing).

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Registration Statement and to the use of our name under the caption “Legal Matters” in the Prospectus included in the Registration Statement.

Very truly yours,

/s/ Jones Walker LLP