Exhibit 32.1

Certification of Chief Executive Officer and Chief Financial Officer

Pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

I, James R. Sulat, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to the best of my knowledge the Quarterly Report of Maxygen, Inc. on Form 10-Q for the quarterly period ended September 30, 2011 fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and that information contained in such Quarterly Report on Form 10-Q fairly presents in all material respects the financial condition and results of operations of Maxygen, Inc.