Many psychological theories posit foundational links between two fundamental constructs: (1) our ability to produce, perceive, and represent action; and (2) our ability to understand the meaning and motivation behind the action (i.e. Theory of Mind; ToM). This position is contentious, however, and long‐standing competing theories of social‐cognitive development debate roles for basic action‐processing in ToM. Developmental research is key to investigating these hypotheses, but whether individual differences in neural and behavioral measures of motor action relate to social‐cognitive development is unknown. We examined 3‐ to 5‐year‐old children's (N = 26) EEG mu‐desynchronization during production of object‐directed action, and explored associations between mu‐desynchronization and children's behavioral motor skills, behavioral action‐representation abilities, and behavioral ToM. For children with high (but not low) mu‐desynchronization, motor skill related to action‐representation abilities, and action‐representation mediated relations between motor skill and ToM. Results demonstrate novel foundational links between action‐processing and ToM, suggesting that basic motor action may be a key mechanism for social‐cognitive development, thus shedding light on the origins and emergence of higher social cognition. We investigated the behavioral and neural correlates of basic motor action to examine associations between these constructs and preschool children's developing theory of mind. Further we sought to clarify the functional correlates of the EEG mu rhythm—a rhythm in the brain that has been hypothesized to index action production as well as action representation, and that may constitute a neural mechanism facilitating links between developments in the motor and social cognitive domains. Results demonstrated that greater mu‐desynchronization moderated relations between action production and action representation skills (contrary to some simplified conceptualizations of mu‐rhythm), and critically also evinced clear links between action and theory of mind: For 3‐ to 5‐year‐old children with high mu‐desynchronization (indicating greater activation of underlying neural populations), action representation mediated the relation between action production and theory of mind, whereby better action production performance predicted better action representation performance which in turn predicted better theory‐of‐mind performance.