Exhibit 32.1

CERTIFICATION OF THE 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 Cempra, Inc. (the “Company”) for the period ended September 30, 2014, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Prabhavathi Fernandes, Ph.D., Chief Executive Officer (Principal Executive Officer) of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to my 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: October 29, 2014

/s/ Prabhavathi Fernandes, Ph.D.

Prabhavathi Fernandes, Ph.D.

Chief Executive Officer (Principal Executive Officer)