  Inclusive $\Upsilon$(1S) and $\Upsilon$(2S) production have been measured in
Pb-Pb collisions at the centre-of-mass energy per nucleon-nucleon pair
$\sqrt{s_{_{\rm NN}}}=5.02$ TeV, using the ALICE detector at the CERN LHC. The
$\Upsilon$ mesons are reconstructed in the centre-of-mass rapidity interval
$2.5<y<4$ and in the transverse-momentum range $p_{\rm T}<15$ GeV/$c$, via
their decays to muon pairs. In this Letter, we present results on the inclusive
$\Upsilon$(1S) nuclear modification factor $R_{\rm AA}$ as a function of
collision centrality, transverse momentum and rapidity. The $\Upsilon$(1S) and
$\Upsilon$(2S) $R_{\rm AA}$, integrated over the centrality range 0-90%, are
$0.37 \pm 0.02 {\rm{(stat)}}\pm 0.03 {\rm{(syst)}}$ and $0.10 \pm 0.04
{\rm{(stat)}}\pm 0.02 {\rm{(syst)}}$, respectively, leading to a ratio
$R_{\rm{AA}}^{\Upsilon(\rm2S)}/R_{\rm{AA}}^{\Upsilon(\rm1S)}$ of
$0.28\pm0.12\text{(stat)}\pm0.06\text{(syst)}$. The observed $\Upsilon$(1S)
suppression increases with the centrality of the collision and no significant
variation is observed as a function of transverse momentum and rapidity.
