Spontaneous face-to-face interactions between mothers and their children play crucial roles in the development of social minds; however, these inter-brain dynamics are still unclear. In this pilot study, we measured MEG mu suppression during face-to-face spontaneous non-linguistic interactions between mothers and their children with autism spectrum disorder (ASD) using the MEG hyperscanning system (i.e., simultaneous recording). The results demonstrated significant correlations between the index of mu suppression (IMS) in the right precentral area and the traits (or severity) of ASD in 13 mothers and 8 children (MEG data from 5 of the children could not be obtained due to motion noise). In addition, higher IMS values (i.e., strong mu suppression) in mothers were associated with higher IMS values in their children. To evaluate the behavioral contingency between mothers and their children, we calculated cross correlations between the magnitude of the mother and child head-motion during MEG recordings. As a result, in mothers whose head motions tended to follow her child's head motion, the magnitudes of mu suppression in the mother's precentral area were large. Further studies with larger sample sizes, including typically developing children, are necessary to generalize this result to typical interactions between mothers and their children.