A bstract The production of ϒ ( nS ) mesons ( n = 1, 2, 3) in p Pb and Pb p collisions at a centre-of-mass energy per nucleon pair $$ \sqrt{s_{\mathrm{NN}}}=8.16 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:msub> <mml:mi>s</mml:mi> <mml:mrow> <mml:mi>N</mml:mi> <mml:mi>N</mml:mi> </mml:mrow> </mml:msub> </mml:msqrt> <mml:mo>=</mml:mo> <mml:mn>8.16</mml:mn> </mml:math> 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 (1 S ) and ϒ (2 S ) states, their forward-to-backward ratios and nuclear modification factors. The measurements are performed as a function of the transverse momentum p T and rapidity in the nucleon-nucleon centre-of-mass frame y * of the ϒ ( nS ) states, in the kinematic range p T &lt; 25 GeV/ c and 1.5 &lt; y * &lt; 4.0 (−5.0 &lt; y * &lt; −2.5) for p Pb (Pb p ) collisions. In addition, production cross-sections for ϒ (3 S ) 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.