A search is presented for single production of a vector-like quark that decays into a Higgs boson and a quark. The search uses a dataset corresponding to 79.8 fb of collisions at TeV collected during 2015-2017 with the ATLAS detector at the Large Hadron Collider. The analysis focuses on the presence of a Higgs boson that decays into two photons, a high-momentum -jet and a forward jet, characteristic of -channel production of the signal process. The main background process is non-resonant diphoton production, with additional small contributions from Standard Model processes containing decays. No significant excess above the background expectation is observed, and upper limits on the signal production cross section are set as a function of the -quark mass. Assuming a generalized coupling and doublet branching ratios of 50% for and , quarks with masses less than 1210 GeV are excluded at the 95% confidence level.