Dancing and singing to music involve auditory-motor coordination and have been essential to our human culture since ancient times. Although scholars have been trying to understand the evolutionary and developmental origin of music, early human developmental manifestations of auditory-motor interactions in music have not been fully investigated. Here we report limb movements and vocalizations in three- to four-months-old infants while they listened to music and were in silence. In the group analysis, we found no significant increase in the amount of movement or in the relative power spectrum density around the musical tempo in the music condition compared to the silent condition. Intriguingly, however, there were two infants who demonstrated striking increases in the rhythmic movements via kicking or arm-waving around the musical tempo during listening to music. Monte-Carlo statistics with phase-randomized surrogate data revealed that the limb movements of these individuals were significantly synchronized to the musical beat. Moreover, we found a clear increase in the formant variability of vocalizations in the group during music perception. These results suggest that infants at this age are already primed with their bodies to interact with music via limb movements and vocalizations.