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. 333-00000) pertaining to the First Financial Bankshares, Inc. 2015 Restricted Stock Plan of our reports dated February 20, 2015, with respect to the consolidated financial statements and the effectiveness of internal control over financial reporting of First Financial Bankshares, Inc. included in its Annual Report (Form 10-K) for the year ended December 31, 2014, filed with the Securities and Exchange Commission.

/s/ Ernst & Young, LLP

Dallas, Texas

July 1, 2015