Neonatal Intensive Care Units (NICU) provide special equipment designed to give life support for the increasing number of prematurely born infants and assure their survival. More recently NICU's strive to include developmentally oriented care and modulate sensory input for preterm infants. Music, among other sensory stimuli, has been introduced into NICUs, but without knowledge on the basic music processing in the brain of preterm infants. In this study, we explored the cortico-subcortical music processing of different types of conditions (Original music, Tempo modification, Key transposition) in newborns shortly after birth to assess the effective connectivity of the primary auditory cortex with the entire newborn brain. Additionally, we investigated if early exposure during NICU stay modulates brain processing of music in preterm infants at term equivalent age. We approached these two questions using Psychophysiological Interaction (PPI) analyses. A group of preterm infants listened to music (Original music) starting from 33 weeks postconceptional age until term equivalent age and were compared to two additional groups without music intervention; preterm infants and full-term newborns. Auditory cortex functional connectivity with cerebral regions known to be implicated in tempo and familiarity processing were identified only for preterm infants with music training in the NICU. Increased connectivity between auditory cortices and thalamus and dorsal striatum may not only reflect their sensitivity to the known music and the processing of its tempo as familiar, but these results are also compatible with the hypothesis that the previously listened music induces a more arousing and pleasant state. Our results suggest that music exposure in NICU's environment can induce brain functional connectivity changes that are associated with music processing.