The nuclear modification factor of neutral pions is measured in proton-lead collisions collected at a center-of-mass energy per nucleon of 8.16 TeV with the LHCb detector. The π^{0} production cross section is measured differentially in transverse momentum (p_{T}) for 1.5<p_{T}<10.0 GeV and in center-of-mass pseudorapidity (η_{c.m.}) regions 2.5<η_{c.m.}<3.5 (forward) and -4.0<η_{c.m.}<-3.0 (backward) defined relative to the proton beam direction. The forward measurement shows a sizable suppression of π^{0} production, while the backward measurement shows the first evidence of π^{0} enhancement in proton-lead collisions at the LHC. Together, these measurements provide precise constraints on models of nuclear structure and particle production in high-energy nuclear collisions.