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-4) and related Prospectus of First Financial Bankshares, Inc. for the registration of 6,275,806 of its shares of its common stock and to the incorporation by reference therein of our reports dated February 19, 2019, with respect to the consolidated financial statements of First Financial Bankshares, Inc. and subsidiaries, and the effectiveness of internal control over financial reporting of First Financial Bankshares, Inc. and subsidiaries included 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

Dallas, Texas

October 18, 2019