  The inclusive production rates of isolated, prompt photons in $p$+Pb
collisions at $\sqrt{s_\mathrm{NN}} = 8.16$ TeV are studied with the ATLAS
detector at the Large Hadron Collider using a dataset with an integrated
luminosity of 165 nb$^{-1}$ recorded in 2016. The cross-section and nuclear
modification factor $R_{p\mathrm{Pb}}$ are measured as a function of photon
transverse energy from 20 GeV to 550 GeV and in three nucleon-nucleon
centre-of-mass pseudorapidity regions, (-2.83,-2.02), (-1.84,0.91), and
(1.09,1.90). The cross-section and $R_{p\mathrm{Pb}}$ values are compared with
the results of a next-to-leading-order perturbative QCD calculation, with and
without nuclear parton distribution function modifications, and with
expectations based on a model of the energy loss of partons prior to the hard
scattering. The data disfavour a large amount of energy loss and provide new
constraints on the parton densities in nuclei.
