The first observation of Z boson production in proton-lead collisions at a centre-of-mass energy per proton-nucleon pair of $$ \sqrt{s_{N\;N}} $$ = 5 TeV is presented. The data sample corresponds to an integrated luminosity of 1.6 nb−1 collected with the LHCb detector. The Z candidates are reconstructed from pairs of oppositely charged muons with pseudorapidities between 2.0 and 4.5 and transverse momenta above 20 GeV/c. The invariant dimuon mass is restricted to the range 60 − 120 GeV/c. The Z production cross-section is measured to be $$ {\sigma_Z}_{\to {\mu}^{+}{\mu}^{-}}\left(\mathrm{fwd}\right)={13.5}_{-4.0}^{+5.4}\left(\mathrm{stat}.\right)\pm 1.2\left(\mathrm{syst}.\right)\mathrm{nb} $$ in the direction of the proton beam and $$ {\sigma}_{Z\to {\mu}^{+}{\mu}^{-}}\left(\mathrm{bwd}\right)={10.7}_{-5.1}^{+8.4}\left(\mathrm{stat}.\right)\pm 1.0\left(\mathrm{syst}.\right)\mathrm{nb} $$ in the direction of the lead beam, where the first uncertainty is statistical and the second systematic.