Exhibit 13.1

Certification by the Principal Executive Officer and Principal Financial Officer pursuant to
18 U.S.C. Section 1350, as adopted pursuant to
Section 906 of the Sarbanes-Oxley Act of 2002

Pursuant to the requirement set forth in Rule 13a-14(b) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and Section 1350 of Chapter 63 of Title 18 of the United States Code (18 U.S.C. §1350), Herve Brailly, Chief Executive Officer of Innate Pharma S.A. (the “Company”), and Frederic Lombard, Chief Financial Officer of the Company, each hereby certifies that, to his knowledge:

(1)The Company’s Annual Report on Form 20-F for the year ended December 31, 2023, to which this Certification is attached as Exhibit 13.1 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Exchange Act, as amended; and

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

Date: April 4, 2024

/s/ Herve Brailly__________________________
Name: Herve Brailly
Title: Chief Executive Officer (Principal Executive Officer)

/s/ Frederic Lombard____________________
Name: Frederic Lombard
Title: Chief Financial Officer (Principal Financial Officer)