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 + , 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 $$ \begin{array}{l}\sigma \left( pp\to {D}^0X\right)=2460\pm 3\pm 130\;\upmu \mathrm{b}\hfill \\ {}\sigma \left( pp\to {D}^{+}X\right)=1000\pm 3\pm 110\;\upmu \mathrm{b}\hfill \\ {}\sigma \left( pp\to {D}_s^{+}X\right)=460\pm 13\pm 100\;\upmu \mathrm{b}\hfill \\ {}\sigma \left( pp\to {D}^{\ast +}X\right)=880\pm 5\pm 140\;\upmu \mathrm{b}\hfill \end{array} $$ where the uncertainties are due to statistical and systematic uncertainties, respectively.