Autism spectrum disorder (ASD) in children is characterized by difficulties in social communication and restricted repetitive behavior patterns. Music therapy appears to have beneficial effects in the area of social interaction and communication. The aim of this systematic literature review is to investigate the effectiveness of music therapy programs on the development of social communication among preschool- and school-aged children with ASD. For this purpose, a detailed study of the relevant literature that has been published in the last decade in peer-reviewed scientific journals was conducted. Web of Science, Springer Link, PsyINFO, and ERIC databases were searched, and according to the eligibility and exclusion criteria, 12 studies were finally selected from the 167 initially found. From the analysis of the results, the following categories were defined to contribute to enhancing social communication: (a) improvisational music therapy; (b) joint attention and eye contact; (c) therapeutic relationship, synchronization, and attunement; (d) imitation; (e) understanding and interaction; (f) family-centered music therapy; and (g) language and socioemotional adjustment. The results of the review were mixed, as music therapy appeared to have a positive effect on improving the social communication of children with ASD, but a general conclusion could not be drawn about the degree of its effectiveness compared to the standard treatments that children usually receive. In the future, further research in this field, especially on the improvisational music Therapy technique, is recommended. Moreover, an increased focus on the development of a common methodological practice regarding the sample selection process and measurement tools is suggested.