The inclusive production rates of isolated, prompt photons in p+Pb collisions at sNN=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 RpPb 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 RpPb 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.