Humans vary substantially in their ability to learn new motor skills. Here, we examined inter-individual differences in learning to play the piano, with the goal of identifying relations to structural properties of white matter fiber tracts relevant to audio-motor learning. Non-musicians (n = 18) learned to perform three short melodies on a piano keyboard in a pure audio-motor training condition (vision of their own fingers was occluded). Initial learning times ranged from 17 to 120 min (mean ± SD: 62 ± 29 min). Diffusion-weighted magnetic resonance imaging was used to derive the fractional anisotropy (FA), an index of white matter microstructural arrangement. A correlation analysis revealed that higher FA values were associated with faster learning of piano melodies. These effects were observed in the bilateral corticospinal tracts, bundles of axons relevant for the execution of voluntary movements, and the right superior longitudinal fasciculus, a tract important for audio-motor transformations. These results suggest that the speed with which novel complex audio-motor skills can be acquired may be determined by variability in structural properties of white matter fiber tracts connecting brain areas functionally relevant for audio-motor learning.