The production of (nS) mesons (n = 1; 2; 3) in p Pb and Pb p collisions at a centre-of-mass energy per nucleon pair p sNN = 8 : 16TeV is measured by the LHCb experiment, using a data sample corresponding to an integrated luminosity of 31.8 nb. The (nS) mesons are reconstructed through their decays into two opposite-sign muons. The measurements comprise the di ff erential production cross-sections of the (1 S) and (2 S) states, their forward-to-backward ratios and nuclear modi fi cation 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 (nS) states, in the kinematic range pT < 25 GeV/ c and 1 : 5 < y < 4 : 0 (5 : 0 < y < 2 : 5) for p Pb (Pb p) collisions. In addition, production cross-sections for (3 S) are measured integrated over phase space and the production ratios between all three (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.