Studies have long observed the bidirectional nature of mother–infant relationships. While behavioral studies have shown that mothers high in social avoidance tendencies can influence the development of these traits in their offspring, the neurophysiological mechanisms underlying this phenomenon, and the role that the infants play, are not well understood. Here we acquired frontal electroencephalogram asymmetry (FA) data simultaneously in 40 mother–infant dyads (Mage mother = 31.6 years; Mage infant = 9 months). Using an actor–partner interdependence model, we examined whether mother (or infant) resting-state FA predicted infant (or mother) FA during two subsequent emotion-eliciting conditions (happy and fear). Maternal social approach versus avoidance traits were assessed as moderators to examine the impact of maternal characteristics on these mother–infant FA relations. In dyads led by mothers with high social avoidance/low social approach characteristics, maternal resting-state FA predicted infant FA during both emotion-eliciting conditions. We did not observe any effects of infant FA on mothers. Therefore, we speculate that individual differences in FA patterns might be a putative brain mechanism through which socially avoidant mothers transfer affective/behavioral information to their infants.