The brain uses internal models to estimate future states of the environment based on current inputs and to predict consequences of planned actions. Neural mechanisms that underlie the acquisition and use of these predictive models are poorly understood. Using a novel experimental paradigm, we show clear evidence for predictive processing in the larval zebrafish brain. We find that when presented with repetitive optic flow stimuli, larval zebrafish modulate their optomotor response by quickly acquiring internal representations of the optic flow pattern. Distinct subcircuits in the cerebellum are involved in the predictive representation of stimulus timing and in using them for motor planning. Evidence for such predictive internal representations appears quickly within two trials, lasts over minute timescales even after optic flow is stopped and quickly adapts to changes in the pattern. These results point to an entrainment-based mechanism that allows the cerebellum to rapidly generate predictive neural signals ultimately leading to faster response times.