Production cross sections of $\Upsilon$(1S), $\Upsilon$(2S), and $\Upsilon$(3S) states decaying into mu(+)mu(-) in proton-lead (pPb) collisions are reported using data collected by the CMS experiment at $\sqrt{; ; ; s_\mathrm{; ; ; NN}; ; ; }; ; ; =$ 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 $\Upsilon$(1S) is found to be $R_\mathrm{; ; ; pPb}; ; ; (\Upsilon(1S))$ = 0.806 $\pm$ 0.024 (stat) $\pm$ 0.059 (syst). Similar results for the excited states indicate a sequential suppression pattern, such that $R_\mathrm{; ; ; pPb}; ; ; (\Upsilon(1S))$ $\gt$ $R_\mathrm{; ; ; pPb}; ; ; (\Upsilon(2S))$ $\gt$ $R_\mathrm{; ; ; pPb}; ; ; (\Upsilon(3S))$. The suppression is much less pronounced in pPb than in PbPb collisions, and independent of transverse momentum $p_\mathrm{; ; ; T}; ; ; ^\Upsilon$ and center-of-mass rapidity $y_\mathrm{; ; ; CM}; ; ; ^\Upsilon$ of the individual $\Upsilon$ state in the studied range $p_\mathrm{; ; ; T}; ; ; ^\Upsilon$ $\lt$ 30 GeV$/c$ and $\vert y_\mathrm{; ; ; CM}; ; ; ^\Upsilon\vert$ $\lt$ 1.93. Models that incorporate sequential suppression of bottomonia in pPb collisions are in better agreement with the data than those which only assume initial-state modifications.