Ferro- and ferrimagnets play host to small-signal, microwave-frequency magnetic excitations called spin waves, the quanta of which are known as magnons. Over the last decade, the field of spin-wave dynamics has contributed much to our understanding of fundamental magnetism. To date, experiments have focussed overwhelmingly on the study of room-temperature systems within classical limits. Here we demonstrate, for the first time, the excitation and detection of propagating spin waves at the single magnon level. Our results allow us to project that coupling of propagating spin-wave excitations to quantum circuits is achievable, enabling fundamental quantum-level studies of magnon systems and potentially opening doors to novel hybrid quantum measurement and information processing devices.