Exhibit 32.1

CERTIFICATION PURSUANT TO
18 U.S.C. SECTION 1350,
AS ADOPTED PURSUANT TO
SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

        In connection with the Annual Report of KYTHERA Biopharmaceuticals, Inc. (the "Company") on Form 10-K for the year ended December 31, 2014, as filed with the Securities and Exchange Commission (the "Report"), Keith R. Leonard, Jr., President and Chief Executive Officer of the Company and John W. Smither, Chief Financial Officer of the Company, respectively, do each hereby certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that

•

The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and



•

The information in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: March 2, 2015

QuickLinks

Exhibit 32.1