Conversational turn-taking is an integral part of language development, as it reflects a confluence of social factors that mitigate communication. Humans coordinate the timing of speech based on the behaviour of another speaker, a behaviour that is learned during infancy. While adults in several primate species engage in vocal turn-taking, the degree to which similar learning processes underlie its development in these non-human species or are unique to language is not clear. We recorded the natural vocal interactions of common marmosets (Callithrix jacchus) occurring with both their sibling twins and parents over the first year of life and observed at least two parallels with language development. First, marmoset turn-taking is a learned vocal behaviour. Second, marmoset parents potentially played a direct role in guiding the development of turn-taking by providing feedback to their offspring when errors occurred during vocal interactions similarly to what has been observed in humans. Though species-differences are also evident, these findings suggest that similar learning mechanisms may be implemented in the ontogeny of vocal turn-taking across our Order, a finding that has important implications for our understanding of language evolution.