Large-scale fiber-based quantum networks will likely employ telecommunication-wavelength photons of around 1550 nm wavelength to exchange quantum information between remote nodes, and quantum memories, ideally operating at the same wavelength, that allow the transmission distances to be increased, as key elements of a quantum repeater. However, the development of a suitable memory remains an ongoing challenge. Here, we demonstrate the storage and reemission of single heralded 1532-nm-wavelength photons using a crystal waveguide. The photons are emitted from a photon-pair source based on spontaneous parametric down-conversion and the memory is based on an atomic frequency comb of 6 GHz bandwidth, prepared through persistent spectral-hole burning of the inhomogeneously broadened absorption line of a cryogenically cooled erbium-doped lithium niobate waveguide. Despite currently limited storage time and efficiency, this demonstration represents an important step toward quantum networks that operate in the telecommunication band and the development of integrated (on-chip) quantum technology using industry-standard crystals.