  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.

High Energy Physics - Experiment;Nuclear Experiment