Ultra-high-energy photons with energies exceeding $10^{17}$ eV offer a wealth of connections to different aspects of cosmic-ray astrophysics as well as to gamma-ray and neutrino astronomy. The recent observations of photons with energies in the $10^{15}$ eV range further motivate searches for even higher-energy photons. In this paper, we present a search for photons with energies exceeding $2{\times}10^{17}$ eV using about 5.5 years of hybrid data from the low-energy extensions of the Pierre Auger Observatory. The upper limits on the integral photon flux derived here are the most stringent ones to date in the energy region between $10^{17}$ and $10^{18}$ eV.