In an early description of the mu rhythm, Gastaut and Bert [Gastaut, H. J., & Bert, J. (1954). EEG changes during cinematographic presentation. Clinical Neurophysiology, 6, 433-444] noted that it was blocked when an individual identified himself with an active person on the screen, suggesting that it may be modulated by the degree to which the individual can relate to the observed action. Additionally, multiple recent studies suggest that the mirror neurons system (MNS) is impaired in individuals with autism spectrum disorders (ASD), which may affect their ability to relate to others. The current study aimed to investigate MNS sensitivity by examining mu suppression to familiarity, i.e., the degree to which the observer is able to identify with the actor on the screen by using familiar versus unfamiliar actors. The participants viewed four 80s videos that included: (1) stranger: an unfamiliar hand performing a grasping action; (2) familiar: the child's guardian or sibling's hand performing the same action; (3) own: the participant's own hand performing the same action; (4) bouncing balls: two balls moving vertically toward and away from each other. The study revealed that mu suppression was sensitive to degree of familiarity. Both typically developing participants and those with ASD showed greater suppression to familiar hands compared to those of strangers. These findings suggest that the MNS responds to observed actions in individuals with ASD, but only when individuals can identify in some personal way with the stimuli.