Exhibit 5.1

[LETTERHEAD OF JONES WALKER LLP]

July 31, 2017

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 (File No. 333-202489) (the “Registration Statement”) 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 shares of common stock of the Company, par value $1.00 per share (the “Common Stock”). This opinion relates to the sale of up to 2,610,304 shares of Common Stock of the Company (the “Shares”) by Banco de Sabadell, S.A. (the “Selling Shareholder”) pursuant to the Registration Rights Agreement dated as of July 31, 2017, by and among the Company and the Selling Shareholder, and the Stock Purchase Agreement dated as of February 28, 2017, by and among the Company, the Selling Shareholder and Sabadell United Bank, N.A.

We have examined the Registration Statement as it became effective under the Securities Act; the Company’s prospectus, dated March 4, 2015 (the “Base Prospectus”), as supplemented by the Company’s prospectus supplement dated July 31, 2017 (together with the Base Prospectus, the “Prospectus”) filed by the Company pursuant to Rule 424(b) of the rules and regulations of the Commission under the Securities Act; the Stock Purchase Agreement; and the Registration Rights Agreement. We have also examined originals, or duplicates or certified or conformed copies, of such records, agreements, documents and other instruments and have made such other investigations as we have deemed appropriate and necessary in connection with the opinion 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 other representatives of the Company.

In rendering the opinion 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.

Based upon the foregoing, and subject to the qualifications, assumptions and limitations stated herein, we are of the opinion that the Shares are validly issued, fully paid and nonassessable.

We do not express any opinion herein concerning any law other than the law of the State of Louisiana.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Current Report on Form 8-K filed by the Company with the Commission on July 31, 2017, and to the use of our name under the caption “Legal Matters” in the Prospectus.

Very truly yours,

/s/ Jones Walker LLP

JONES WALKER LLP