Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the Registration Statement (Form S-8 (No. 333-XXXXX)) pertaining to the IBERIABANK Corporation Amended & Restated 2010 Stock Incentive Plan of our reports dated February 28, 2014, with respect to the consolidated financial statements of IBERIABANK Corporation and the effectiveness of internal control over financial reporting of IBERIABANK Corporation included in its Annual Report (Form 10-K) for the year ended December 31, 2013, filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

New Orleans, Louisiana

August 11, 2014