The production of prompt D^{0} mesons in proton-lead collisions in both the forward and backward rapidity regions at a center-of-mass energy per nucleon pair of sqrt[s_{NN}]=8.16 TeV is measured by the LHCb experiment. The nuclear modification factor of prompt D^{0} mesons is determined as a function of the transverse momentum p_{T}, and the rapidity in the nucleon-nucleon center-of-mass frame y^{*}. In the forward rapidity region, significantly suppressed production with respect to pp collisions is measured, which provides significant constraints on models of nuclear parton distributions and hadron production down to the very low Bjorken-x region of ∼10^{-5}. In the backward rapidity region, a suppression with a significance of 2.0-3.8 standard deviations compared to parton distribution functions in a nuclear environment expectations is found in the kinematic region of p_{T}>6 GeV/c and -3.25<y^{*}<-2.5, corresponding to x∼0.01.