Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the following Registration Statements:

(1) Registration Statement (Form S-8 No. 333-190247) pertaining to the 2012 Incentive Stock Option Plan of First Financial Bankshares, Inc.;

(2) Registration Statement (Form S-8 No. 333-114121) pertaining to the 2002 Incentive Stock Option Plan of First Financial Bankshares, Inc.; and

(3) Registration Statement (Form S-8 No. 333-205406) pertaining to the 2015 Restricted Stock Plan of First Financial Bankshares, Inc;

of our reports dated February 22, 2021, 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 this Annual Report (Form 10-K) of First Financial Bankshares, Inc. for the year ended December 31, 2020.

/s/ Ernst & Young LLP

Dallas, Texas

February 22, 2021