Hybrid interfaces between semiconductor quantum dots and atomic systems could be of potential fundamental and technological interest, because they can combine the advantages of both constituents. Semiconductor quantum dots are tunable and deterministic sources of single and entangled photons. Atomic vapors are widely used as slow-light media and quantum memories. Merging both systems could enable the storage of quantum dot emission—an important step towards the implementation of quantum memories and quantum repeaters. Here, we show a hybrid semiconductor–atomic interface for slowing down single photons emitted from a single quantum dot. We use a double absorption resonance in rubidium vapor to create a slow-light medium in which a single photon is stored for 15 times its temporal width. Our result is the first demonstration of non-classical light storage, where single photons are generated on demand from a semiconductor source.