Avenue Therapeutics (ATXI) 10-Q 2021 Q1 Quarterly report

Exhibit 32.1

Certification of

Principal Executive Officer

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

I, Lucy Lu, M.D., Chief Executive Officer of Avenue Therapeutics, Inc. (the “Company”), in compliance with Section 906 of the Sarbanes-Oxley Act of 2002, hereby certify that, to the best of my knowledge, the Company’s Quarterly Report on Form 10-Q for the period ended March 31, 2021 (the “Report”) filed with the Securities and Exchange Commission:

• Fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

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

/s/ Lucy Lu, M.D.

Lucy Lu, M.D.

President, Chief Executive Officer and Director

(Principal Executive Officer)

May 17, 2021