The transverse momentum (p(T)) distribution for inclusive neutral pions in the very forward rapidity region has been measured, with the Large Hadron Collider forward detector (LHCf), in proton-lead collisions at nucleon-nucleon center-of-mass energies of v sNN = 5.02 TeV at the LHC. The pT spectra obtained in the rapidity range -11.0 < ylab < -8.9 and 0 < pT < 0.6 GeV (in the detector reference frame) show a strong suppression of the production of neutral pions after taking into account ultraperipheral collisions. This leads to a nuclear modification factor value, relative to the interpolated pT spectra in proton-proton collisions at v s = 5.02 TeV, of about 0.1-0.4. This value is compared with the predictions of several hadronic interaction Monte Carlo simulations.