The production of ({W}^{±}) bosons is studied in proton-lead (pPb) collisions at a nucleon-nucleon centre-of-mass energy of (\sqrt{{s}{\mathrm{NN}}}=8.16\phantom{\rule{0.25em}{0ex}}\text{TeV}). Measurements are performed in the ({W}^{±}\to {\mu }^{±}{\nu }{\mu }) channel using a data sample corresponding to an integrated luminosity of (173.4±6.1\phantom{\rule{0.25em}{0ex}}{\text{nb}}^{-1}), collected by the CMS Collaboration at the LHC. The number of positively and negatively charged W bosons is determined separately in the muon pseudorapidity region in the laboratory frame (|{\eta }{\mathrm{lab}}^{\mu }|<2.4) and transverse momentum ({p}{T}^{\mu }>25\phantom{\rule{0.25em}{0ex}}\text{GeV}/c). The ({W}^{±}) boson differential cross sections, muon charge asymmetry, and the ratios of ({W}^{±}) boson yields for the proton-going over the Pb-going beam directions are reported as a function of the muon pseudorapidity in the nucleon-nucleon centre-of-mass frame. The measurements are compared to the predictions from theoretical calculations based on parton distribution functions (PDFs) at next-to-leading-order. The results favour PDF calculations that include nuclear modifications and provide constraints on the nuclear PDF global fits.