In active inference, the sensory surprisal (a log-probability of sensory data) of the prediction error between prediction and sensory input is modulated by action. The urge to move (groove) induced by syncopation, which provides metric prediction errors, can be considered a case of active inference in music perception. The present study investigated whether rhythmic prediction error is modulated by improving the precision of rhythm perception through tapping in sync with the rhythm. Thirty-five participants listened to a rhythmic sequence while tapping two beats (tapping condition) or holding a pillow (no-tapping condition), and electroencephalography (EEG) was recorded. In both conditions, the timing of tone onset was rarely earlier (deviant: 20%) than the standard (80%). The timing deviant elicited mismatch negativity (MMN) in both the tapping and no-tapping conditions, reflecting a prediction error in timing. Moreover, the MMN response, weighted by precision, was larger in the tapping condition than in the no-tapping condition. Neural entrainment was measured by calculating intertrial phase coherence (ITPC), which reflects oscillatory activity synchronized to stimulus frequency, and ITPC differed between the two conditions at beat-related frequencies. These results suggest that tapping enhanced meter and beat information, and reduced the sensory surprisal of syncopation, resulting in a larger precision-weighted prediction error. These effects were not due to physiological arousal differences between conditions, as assessed by EEG power and heart rate variability. This study provides evidence for the modulation of sensory prediction error by bodily engagement within the active inference framework.