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 × 10$^{17}$ eV using about 5.5 yr 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.