Preterm birth disrupts important neurodevelopmental processes occurring from mid-fetal to term-age. Musicotherapy, by enriching infants' sensory input, might enhance brain maturation during this critical period of activity-dependent plasticity. To study the impact of music on preterm infants' brain structural changes, we recruited 54 very preterm infants randomized to receive or not a daily music intervention, that have undergone a longitudinal multi-shell diffusion MRI acquisition, before the intervention (at 33 weeks' gestational age) and after it (at term-equivalent-age). Using whole-brain fixel-based (FBA) and NODDI analysis (n = 40), we showed a longitudinal increase of fiber cross-section (FC) and fiber density (FD) in all major cerebral white matter fibers. Regarding cortical grey matter, FD decreased while FC and orientation dispersion index (ODI) increased, reflecting intracortical multidirectional complexification and intracortical myelination. The music intervention resulted in a significantly higher longitudinal increase of FC and ODI in cortical paralimbic regions, namely the insulo-orbito-temporopolar complex, precuneus/posterior cingulate gyrus, as well as the auditory association cortex. Our results support a longitudinal early brain macro and microstructural maturation of white and cortical grey matter in preterm infants. The music intervention led to an increased intracortical complexity in regions important for socio-emotional development, known to be impaired in preterm infants.