The production cross-sections of ϒ(1S), ϒ(2S) and ϒ(3S) mesons in proton-proton collisions at s=13 TeV are measured with a data sample corresponding to an integrated luminosity of 277 ± 11 pb−1 recorded by the LHCb experiment in 2015. The ϒ mesons are reconstructed in the decay mode ϒ → μ+μ−. The differential production cross-sections times the dimuon branching fractions are measured as a function of the ϒ transverse momentum, pT, and rapidity, y, over the range 0 < pT< 30 GeV/c and 2.0 < y < 4.5. The ratios of the cross-sections with respect to the LHCb measurement at s=8 TeV are also determined. The measurements are compared with theoretical predictions based on NRQCD.