EXHIBIT 13.1

PRINCIPAL EXECUTIVE OFFICER CERTIFICATION

PURSUANT TO 18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO SECTION 906 OF THE

SARBANES-OXLEY ACT OF 2002

I, Jan G. van de Winkel, President and Chief Executive Officer of Genmab A/S, certify, pursuant to 18 U.S.C. §1350, as adopted pursuant to §906 of the Sarbanes-Oxley Act of 2002, that, to the best of my knowledge:

        (1)   The Annual Report on Form 20-F of Genmab A/S for the period ended December 31, 2019 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

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