Many of the sensations experienced by an organism are caused by their own actions, yet it remains largely unknown how the brain recognizes self-generated sensations. We trained mice to expect the precisely timed acoustic outcome of a forelimb movement using a closed-loop sound-generating lever. Dense neuronal recordings in the auditory cortex revealed suppression of responses to self-generated sounds that was specific to the expected acoustic features, specific to a precise time within the movement, and specific to the movement that was coupled to sound during training. Recording in the absence of sound revealed movement-related signals that encoded the expected frequency and time of the omitted sound. Together, these findings reveal that predictive processing in the mouse auditory cortex is consistent with a learned internal model linking a specific action to its temporally precise acoustic outcome.