During speech processing, neural activity in non-autistic adults and infants tracks the speech envelope. Recent research in adults indicates that this neural tracking relates to linguistic knowledge and may be reduced in autism. Such reduced tracking, if present already in infancy, could impede language development. In the current study, we focused on children with a family history of autism, who often show a delay in first language acquisition. We investigated whether differences in tracking of sung nursery rhymes during infancy relate to language development and autism symptoms in childhood. We assessed speech-brain coherence at either 10 or 14 months of age in a total of 22 infants with high likelihood of autism due to family history and 19 infants without family history of autism. We analyzed the relationship between speech-brain coherence in these infants and their vocabulary at 24 months as well as autism symptoms at 36 months. Our results showed significant speech-brain coherence in the 10- and 14-month-old infants. We found no evidence for a relationship between speech-brain coherence and later autism symptoms. Importantly, speech-brain coherence in the stressed syllable rate (1–3 Hz) predicted later vocabulary. Follow-up analyses showed evidence for a relationship between tracking and vocabulary only in 10-month-olds but not in 14-month-olds and indicated possible differences between the likelihood groups. Thus, early tracking of sung nursery rhymes is related to language development in childhood.