To study emotional reactions to music, it is important to consider the temporal dynamics of both affective responses and underlying brain activity. Here, we investigated emotions induced by music using functional magnetic resonance imaging (fMRI) with a data-driven approach based on intersubject correlations (ISC). This method allowed us to identify moments in the music that produced similar brain activity (i.e. synchrony) among listeners under relatively natural listening conditions. Continuous ratings of subjective pleasantness and arousal elicited by the music were also obtained for the music outside of the scanner. Our results reveal synchronous activations in left amygdala, left insula and right caudate nucleus that were associated with higher arousal, whereas positive valence ratings correlated with decreases in amygdala and caudate activity. Additional analyses showed that synchronous amygdala responses were driven by energy-related features in the music such as root mean square and dissonance, while synchrony in insula was additionally sensitive to acoustic event density. Intersubject synchrony also occurred in the left nucleus accumbens, a region critically implicated in reward processing. Our study demonstrates the feasibility and usefulness of an approach based on ISC to explore the temporal dynamics of music perception and emotion in naturalistic conditions.