A crucial aspect of auditory perception is the ability to use sound cues to predict future events and to time actions accordingly. For example, distinct smartphone notification sounds reflect a call that needs to be answered within a few seconds, or a text that can be read later; the sound of an approaching vehicle signals when it is safe to cross the street. Other animals similarly use sounds to plan, time and execute behaviors such as hunting, evading predation and tending to offspring. However, the neural mechanisms that underlie sound-guided prediction of upcoming salient event timing are not well understood. To address this gap, we employed an appetitive sound-triggered reward time prediction behavior in head-fixed mice. We find that mice trained on this task reliably estimate the time from a sound cue to upcoming reward on the scale of a few seconds, as demonstrated by learning-dependent well-timed increases in reward-predictive licking. Moreover, mice showed a dramatic impairment in their ability to use sound to predict delayed reward when the auditory cortex was inactivated, demonstrating its causal involvement. To identify the neurophysiological signatures of auditory cortical reward-timing prediction, we recorded local field potentials during learning and performance of this behavior and found that the magnitude of auditory cortical responses to the sound prospectively encoded the duration of the anticipated sound-reward time interval. Next, we explored how and where these sound-triggered time interval prediction signals propagate from the auditory cortex to time and initiate consequent action. We targeted the monosynaptic projections from the auditory cortex to the posterior striatum and found that chemogenetic inactivation of these projections impairs animal's ability to predict sound-triggered delayed reward. Simultaneous neural recordings in the auditory cortex and posterior striatum during task performance revealed coordination of neural activity across these regions during the sound cue predicting the time interval to reward. Collectively, our findings identify an auditory cortical-striatal circuit supporting sound-triggered timing-prediction behaviors.