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 ${\ensuremath{\pi}}^{0}$ production cross section is measured differentially in transverse momentum (${p}_{T}$) for $1.5<{p}_{T}<10.0\text{ }\text{ }\mathrm{GeV}$ and in center-of-mass pseudorapidity (${\ensuremath{\eta}}_{\mathrm{c}.\mathrm{m}.}$) regions $2.5<{\ensuremath{\eta}}_{\mathrm{c}.\mathrm{m}.}<3.5$ (forward) and $\ensuremath{-}4.0<{\ensuremath{\eta}}_{\mathrm{c}.\mathrm{m}.}<\ensuremath{-}3.0$ (backward) defined relative to the proton beam direction. The forward measurement shows a sizable suppression of ${\ensuremath{\pi}}^{0}$ production, while the backward measurement shows the first evidence of ${\ensuremath{\pi}}^{0}$ 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.