Yawn contagion in humans has been proposed to be related to our capacity for empathy. It is presently unclear whether this capacity is uniquely human or shared with other primates, especially monkeys. Here, we show that in gelada baboons (Theropithecus gelada) yawning is contagious between individuals, especially those that are socially close, i.e., the contagiousness of yawning correlated with the level of grooming contact between individuals. This correlation persisted after controlling for the effect of spatial association. Thus, emotional proximity rather than spatial proximity best predicts yawn contagion. Adult females showed precise matching of different yawning types, which suggests a mirroring mechanism that activates shared representations. The present study also suggests that females have an enhanced sensitivity and emotional tuning toward companions. These findings are consistent with the view that contagious yawning reveals an emotional connection between individuals. This phenomenon, here demonstrated in monkeys, could be a building block for full-blown empathy.