This article presents the first measurement of the differential Z-boson production cross-section in the forward region using proton-lead collisions with the LHCb detector. The dataset was collected at a nucleon-nucleon centre-of-mass energy of root(NN)-N-s = 8.16TeV in 2016, corresponding to an integrated luminosity of 30.8 nb(-1). The forward-backward ratio and the nuclear modification factors are measured together with the differential crosssection as functions of the Z boson rapidity in the centre-of-mass frame, the transverse momentum of the Z boson and a geometric variable phi*. The results are in good agreement with the predictions from nuclear parton distribution functions, providing strong constraining power at small Bjorken-x.