Social dominance hierarchies play a pivotal role in shaping the behaviour of many species, and sex differences within these hierarchies often exist. To date, however, few physical markers of dominance have been identified. Such markers would be valuable in terms of understanding the etiology of dominant behaviour and changes in social hierarchies over time. Animals may also use such traits to evaluate the potential dominance of others relative to themselves (i.e. a physical “cue”). Facial width-to-height ratio (fWHR), for example, has been suggested as a cue to dominance in humans, with links to both dominant behaviour and the perception of dominance in other individuals. Whether this association is present in non-human animals is currently not known. Therefore, here we examine within-species links between fWHR and dominant behaviour in 64 brown capuchin monkeys (Sapajus spp.) aged between 2 and 40 years. fWHR was positively associated with alpha status and with a dimensional rating of assertive personality in both males and females. Moreover, fWHR showed significant sexual dimorphism in adults but not juveniles, suggesting a developmental change may occur during puberty. In a sub-sample, sex differences were mediated by weight, suggesting fWHR dimorphism does not exceed what would be expected by differences in body weight. This is the first report of an association between face shape and behaviour in a non-human species. Results are discussed in terms of the role that face-behaviour associations might play within capuchin societies, and the possible selective forces that might have led to the evolution of fWHR-dominance associations in humans.