The production cross sections for prompt open-charm mesons in proton-proton collisions at a center-of-mass energy of 13 TeV are reported. The measurement is performed using a data sample collected by the CMS experiment corresponding to an integrated luminosity of 29 nb−1. The differential production cross sections of the D∗±, D±, and D0 $$ \left({\overline{\mathrm{D}}}^0\right) $$mesons are presented in ranges of transverse momentum and pseudorapidity 4 < pT < 100 GeV and |η| < 2.1, respectively. The results are compared to several theoretical calculations and to previous measurements.