Quantum memory networks as an intermediate stage in the development of a quantum internet will enable a number of significant applications. To connect and entangle remote quantum memories, it is best to use photons. In previous experiments, entanglement of two memory nodes has been achieved via photon interference. Going beyond the state of the art by entangling many quantum nodes at a distance is highly sought after. Here, we report the entanglement of three remote quantum memories via three-photon interference. We employ laser-cooled atomic ensembles and make use of a ring cavity to enhance the overall efficiency of our memory–photon entanglement. By interfering three single photons from three separate set-ups, we create entanglement of three memories and three photons. Then, by measuring the photons and applying feed-forward, we achieve heralded entanglement between the three memories. Our experiment may be employed as a building block to construct larger and complex quantum networks.