The assessment of relatedness may be crucial in the evolution of socio-sexual behaviour, because it can be associated with fitness benefits mediated by both nepotism and inbreeding avoidance. In this context, one proposed mechanism for kin recognition is ‘phenotype matching’; animals might compare phenotypic similarities between themselves and others in order to assess the probability that they are related. Among cues potentially used for kin discrimination, body odours constitute interesting candidates that have been poorly investigated in anthropoid primates so far, because of a mixture of theoretical considerations and methodological/experimental constraints. In this study, we used an indirect approach to examine the similarity in odour signals emitted by related individuals from a natural population of chacma baboons (Papio ursinus). For that purpose, we designed an innovative behavioural tool using mice olfactory abilities in a habituation–discrimination paradigm. We show that: (i) mice can detect odour differences between individuals of same sex and age class in another mammal species, and (ii) mice perceive a higher odour similarity between related baboons than between unrelated baboons. These results suggest that odours may play a role in both the signalling of individual characteristics and of relatedness among individuals in an anthropoid primate. The ‘biological olfactometer’ developed in this study offers new perspectives to the exploration of olfactory signals from a range of species.