Instrumental music and language are both syntactic systems, employing complex, hierarchically-structured sequences built using implicit structural norms. This organization allows listeners to understand the role of individual words or tones in the context of an unfolding sentence or melody. Previous studies suggest that the brain mechanisms of syntactic processing may be partly shared between music and language. However, functional neuroimaging evidence for anatomical overlap of brain activity involved in linguistic and musical syntactic processing has been lacking. In the present study we used functional magnetic resonance imaging (fMRI) in conjunction with an interference paradigm based on sung sentences. We show that the processing demands of musical syntax (harmony) and language syntax interact in Broca's area in the left inferior frontal gyrus (without leading to music and language main effects). A language main effect in Broca's area only emerged in the complex music harmony condition, suggesting that (with our stimuli and tasks) a language effect only becomes visible under conditions of increased demands on shared neural resources. In contrast to previous studies, our design allows us to rule out that the observed neural interaction is due to: (1) general attention mechanisms, as a psychoacoustic auditory anomaly behaved unlike the harmonic manipulation, (2) error processing, as the language and the music stimuli contained no structural errors. The current results thus suggest that two different cognitive domains-music and language-might draw on the same high level syntactic integration resources in Broca's area.