We demonstrate a single-photon stored-light interferometer, where a photon is stored in a laser-cooled atomic ensemble in the form of a Rydberg polariton with a spatial extent of 10×1×1µm3. The photon is subject to a Ramsey sequence, i.e., "split" into a superposition of two paths. After a delay of up to 450 ns, the two paths are recombined to give an output dependent on their relative phase. The superposition time of 450 ns is equivalent to a free-space propagation distance of 135 m. We show that the interferometer fringes are sensitive to external fields and suggest that stored-light interferometry could be useful for localized sensing applications.