Production cross sections of Υ(1S), Υ(2S), and Υ(3S) states decaying into μ+μ− in proton-lead (pPb) collisions are reported using data collected by the CMS experiment at √sNN = 5.02 TeV. A comparison is made with corresponding cross sections obtained with pp data measured at the same collision energy and scaled by the Pb nucleus mass number. The nuclear modification factor for Υ(1S) is found to be RpPb(Υ(1S)) = 0.806±0.024 (stat)±0.059 (syst). Similar results for the excited states indicate a sequential suppression pattern, such that RpPb(Υ(1S)) > RpPb(Υ(2S)) > RpPb(Υ(3S)). The suppression of all states is much less pronounced in pPb than in PbPb collisions, and independent of transverse momentum pΥT and center-of-mass rapidity yΥCM of the individual Υ state in the studied range p ΥT < 30 GeV/c and |yΥCM| <1.93. Models that incorporate final-state effects of bottomonia in pPb collisions are in better agreement with the data than those which only assume initial-state modifications.