This study aimed to evaluate the effectiveness of music therapy (MT) for children with co-occurring autism spectrum disorder (ASD) and intellectual disabilities (ID) and explore whether pre-intervention quantitative electroencephalogram (qEEG) responses can predict outcomes. A randomized controlled trial was conducted with 33 children receiving MT and 34 receiving an active control therapy. Participants received either MT or a non-musical social skills intervention for 45 min weekly over 12 weeks. Primary outcomes were measured using the Childhood Autism Rating Scale (CARS-2), along with the parent-rated Social Responsiveness Scale (SRS-2) and video coding of social behaviors. Both conditions significantly improved in CARS-2 scores at 2 weeks and 4 months post-intervention, with no differences between MT and control conditions. No changes were found in SRS-2 scores. While both conditions showed reduced disengagement after intervention, only the MT condition showed increased engagement and initiation. Strong qEEG responses to social scenes and music predicted increased initiation, indicating its potential to help tailor interventions. These results support incorporating MT into standard services and further research on qEEG predictors.