Independent Bank (IBTX) 8-K Audited Consolidated Financial Statements of

Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in the Registration Statement on FormS-3 of Independent Bank Group, Inc. (RegistrationNo. 333-218782) and the Registration Statement on FormS-8 of Independent Bank Group, Inc. (RegistrationNo. 333-198483) of our report dated October 2, 2019 on the consolidated financial statements of Guaranty Bancorp, which is included in this Current Report on Form8-K.

/s/ Crowe LLP

Oak Brook, Illinois

January 21, 2020