EXHIBIT 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the reference to our firm under the caption “Experts” in the Registration Statement (Form S-3) and related Prospectus of IBERIABANK Corporation and subsidiaries for the registration of common stock, serial preferred stock, depositary shares, rights, warrants, and units and to the incorporation by reference therein of our reports dated February 22, 2019, with respect to the consolidated financial statements of IBERIABANK Corporation, and the effectiveness of internal control over financial reporting of IBERIABANK Corporation incorporated by reference in its Annual Report (Form 10-K) for the year ended December 31, 2018, filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

New Orleans, Louisiana

March 28, 2019