  The transverse momentum ($p_\text{T}$) 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 $\sqrt{s_{NN}} = 5.02$TeV at the
LHC. The $p_\text{T}$ spectra obtained in the rapidity range $-11.0 <
y_\text{lab} < -8.9$ and $0 < p_\text{T} < 0.6$GeV
  (in the detector reference frame) show a strong suppression of the production
of neutral pions after taking into account ultra-peripheral collisions. This
leads to a nuclear modification factor value, relative to the interpolated
$p_\text{T}$ spectra in proton-proton collisions at $\sqrt{s} = 5.02$TeV, of
about 0.1--0.4. This value is compared with the predictions of several hadronic
interaction Monte Carlo simulations.
