Music learning has received increasing attention in the last decades due to the variety of functions and brain plasticity effects involved during its practice. Most previous reports interpreted the differences between music experts and laymen as the result of training. However, recent investigations suggest that these differences are due to a combination of genetic predispositions with the effect of music training. Here, we tested the relationship of the dorsal auditory-motor pathway with individual behavioural differences in short-term music learning. We gathered structural neuroimaging data from 44 healthy non-musicians (28 females) before they performed a rhythm- and a melody-learning task during a single behavioural session, and manually dissected the arcuate fasciculus (AF) in both hemispheres. The macro- and microstructural organization of the AF (i.e., volume and FA) predicted the learning rate and learning speed in the musical tasks, but only in the right hemisphere. Specifically, the volume of the right anterior segment predicted the synchronization improvement during the rhythm task, the FA in the right long segment was correlated with the learning rate in the melody task, and the volume and FA of the right whole AF predicted the learning speed during the melody task. This is the first study finding a specific relation between different branches within the AF and rhythmic and melodic materials. Our results support the relevant function of the AF as the structural correlate of both auditory-motor transformations and the feedback-feedforward loop, and suggest a crucial involvement of the anterior segment in error-monitoring processes related to auditory-motor learning. These findings have implications for both the neuroscience of music field and second-language learning investigations.