Background/Objectives: The aim of this systematic review is to assess the effect of music therapy initiated during neonatal intensive care unit (NICU) hospitalization on the early neurodevelopment of infants and to evaluate its impact on functional improvements in children with neurological deficits. Numerous studies underscore the benefits of neurological music therapy (NMT) for treating various neurological conditions. Methods: This systematic review (SR) specifically includes randomized controlled trials (RCTs) and draws from a comprehensive search of articles in the Scopus and MEDLINE databases. Eligible studies examined the effects of NMT on infants and children with central nervous system static lesions. Eighteen studies met all inclusion criteria, and the overall quality of the evidence was high. Results: However, while NMT appears to be well-tolerated by most neonates and children and holds promise for enhancing functional and physiological development, its impact on specific biomarkers in neurological conditions remains underexplored. Further research is essential to clarify NMT’s potential role in rehabilitation and to optimize therapeutic approaches for neurological support.