The production of ϒ(nS) mesons (n = 1, 2, 3) in pPb and Pbp collisions at a centre-of-mass energy per nucleon pair sNN−−−√=8.16 TeV is measured by the LHCb experiment, using a data sample corresponding to an integrated luminosity of 31.8 nb−1. The ϒ(nS) mesons are reconstructed through their decays into two opposite-sign muons. The measurements comprise the differential production cross-sections of the ϒ(1S) and ϒ(2S) states, their forward-to-backward ratios and nuclear modification factors. The measurements are performed as a function of the transverse momentum pT and rapidity in the nucleon-nucleon centre-of-mass frame y* of the ϒ(nS) states, in the kinematic range pT < 25 GeV/c and 1.5 < y* < 4.0 (−5.0 < y* < −2.5) for pPb (Pbp) collisions. In addition, production cross-sections for ϒ(3S) are measured integrated over phase space and the production ratios between all three ϒ(nS) states are determined. Suppression for bottomonium in proton-lead collisions is observed, which is particularly visible in the ratios. The results are compared to theoretical models.