Production cross-sections of prompt charm mesons are measured with the first data from pp collisions at the LHC at a centre-of-mass energy of 13 TeV. The data sample corresponds to an integrated luminosity of 4.98 +/- 0.19 pb(-1) collected by the LHCb experiment. The production cross-sections of D-0, D+, D (s) (+) , and D*+ mesons are measured in bins of charm meson transverse momentum, p(T), and rapidity, y, and cover the range 0 < p(T) < 15GeV/c and 2.0 < y < 4.5. The inclusive cross-sections for the four mesons, including charge conjugation, within the range of 1 < p(T) < 8 GeV/c are found to be sigma(pp -> D-0 X) = 2460 +/- 3 +/- 130 mu b sigma(pp -> D+ X) = 1000 +/- 3 +/- 110 mu b sigma(pp -> Ds+X) = 460 +/- 13 +/- 100 mu b sigma(pp -> D*+ X) = 880 +/- 5 +/- 140 mu b where the uncertainties are due to statistical and systematic uncertainties, respectively.