  Production of $\Upsilon$ mesons in proton-lead collisions at a
nucleon-nucleon centre-of-mass energy $\sqrt{s_{NN}}=5 \mathrm{TeV}$ is studied
with the LHCb detector. The analysis is based on a data sample corresponding to
an integrated luminosity of $1.6 \mathrm{nb}^{-1}$. The $\Upsilon$ mesons of
transverse momenta up to $15 \mathrm{GeV}/c$ are reconstructed in the dimuon
decay mode. The rapidity coverage in the centre-of-mass system is $1.5<y<4.0$
(forward region) and $-5.0<y<-2.5$ (backward region). The forward-backward
production ratio and the nuclear modification factor for $\Upsilon(1S)$ mesons
are determined. The data are compatible with the predictions for a suppression
of $\Upsilon(1S)$ production with respect to proton-proton collisions in the
forward region, and an enhancement in the backward region. The suppression is
found to be smaller than in the case of prompt $J/\psi$ mesons.
