Pragmatic theories of communication assume that humans evolved a species-unique inferential capacity to express and recognize intentions via communicative actions. We show that 13-month-old non-verbal infants can interpret the turn-taking exchange of variable tone sequences between unfamiliar agents as indicative of communicative transfer of goal-relevant information from a knowledgeable to a naïve agent pursuing the goal. No such inference of information transfer was drawn by the infants, however, when a) the agents exchanged fully predictable identical signal sequences, which does not enable transmission of new information, or b) when no goal-relevant contextual change was observed that would motivate its communicative transmission. These results demonstrate that young infants can recognize communicative interactions between third-party agents and possess an evolved capacity for communicative mind-reading that enables them to infer what contextually relevant information has been transmitted between the agents even without language.