The active role of sleep in memory consolidation is still debated, and due to a large between-species variation, the investigation of a wide range of different animal species (besides humans and laboratory rodents) is necessary. The present study applied a fully non-invasive methodology to study sleep and memory in domestic dogs, a species proven to be a good model of human awake behaviours. Polysomnography recordings performed following a command learning task provide evidence that learning has an effect on dogs' sleep EEG spectrum. Furthermore, spectral features of the EEG were related to post-sleep performance improvement. Testing an additional group of dogs in the command learning task revealed that sleep or awake activity during the retention interval has both short- and long-term effects. This is the first evidence to show that dogs' human-analogue social learning skills might be related to sleep-dependent memory consolidation.