Measurements are presented of differential cross sections for the production of Z bosons in association with at least one jet initiated by a charm quark in pp collisions at s = 13 TeV. The data recorded by the CMS experiment at the LHC correspond to an integrated luminosity of 35.9 fb−1. The final states contain a pair of electrons or muons that are the decay products of a Z boson, and a jet consistent with being initiated by a charm quark produced in the hard interaction. Differential cross sections as a function of the transverse momentum pT of the Z boson and pT of the charm jet are compared with predictions from Monte Carlo event generators. The inclusive production cross section 405.4 ± 5.6 (stat) ± 24.3 (exp) ± 3.7 (theo) pb, is measured in a fiducial region requiring both leptons to have pseudorapidity |η| < 2.4 and pT> 10 GeV, at least one lepton with pT> 26 GeV, and a mass of the pair in the range 71–111 GeV, while the charm jet is required to have pT> 30 GeV and |η| < 2.4. These are the first measurements of these cross sections in proton-proton collisions at 13 TeV. [Figure not available: see fulltext.]