Exhibit 32.1

Certification of Chief Executive Officer

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 quarterly report on Form 10-Q of Tetraphase Pharmaceuticals, Inc. (the “Company”) for the period ended June 30, 2018, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), Guy Macdonald, as Chief Executive Officer of the Company, hereby certifies, 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 his knowledge:

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

(2) the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: August 2, 2018

/s/ Guy Macdonald 

Guy Macdonald

Chief Executive Officer