In human societies, ritualized greeting behavior includes gestural and vocal displays to signal the social acceptance of an encountering person. These displays are universal across cultures suggesting a pre-human origin. Vocal greeting displays are only reported for monkeys and apes with complex social systems, but none of these studies confirmed that greeting signals fulfill all criteria characterizing human greeting behavior. In this study, we analyzed for the first time whether vocal exchanges between mother and infants in a non-human primate fulfill the criteria of human greeting behavior and whether vocal greeting behavior is present in a basal primate with a less complex social system, the gray mouse lemur. By comparing spontaneous leave-takings and reunions, we found that vocal exchanges during mother-infant reunions fulfilled all six criteria characterizing human greeting behavior. Thus, predictable reciprocal vocal exchanges occurred at the start of the reunion (but not during leave-taking), when mother and infant had visual contact to each other. Thus, we argued that mother-infant vocal exchanges governing reunions are essential to establish social bonds and to ritualize the greeting function. Our findings suggest that ritualized vocal greeting has its origins deeply rooted in mammalian phylogeny and derives from vocal exchanges during parent-infant reunions.