Exhibit 32.1

Section 1350 Certification of the

Chief Executive Officer

Pursuant to Subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code in accordance with Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned, Phillip D. Green, Chief Executive Officer, of Cullen/Frost Bankers, Inc. (the “Corporation”), hereby certifies, to his knowledge, that the Corporation’s Annual Report on Form 10-K for the year ended December 31, 2021 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, and that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Corporation.

/s/ Phillip D. Green	February 4, 2022
Phillip D. Green

The forgoing certification is being furnished solely pursuant to Subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code in accordance with Section 906 of the Sarbanes-Oxley Act of 2002 and shall not be deemed “filed” for purposes of Section 18 of the Securities Exchange Act of 1934, or otherwise subject to the liability of that section, and shall not be deemed to be incorporated by reference into any filing under the Securities Act of 1933 or the Securities Exchange Act of 1934.