Our motor system can generate representations which carry information about the goals of another agent's actions. However, it is not known whether motor representations play a deeper role in social understanding, and, in particular, whether they enable tracking others' beliefs. Here we show that, for adult observers, reliably manifesting an ability to track another's false belief critically depends on representing the agent's potential actions motorically. One signature of motor representations is that they can be disrupted by constraints on an observed agent's action capacities. We therefore used a `mummification' technique to manipulate whether the agent in a visual ball-detection task was free to act or whether he was visibly constrained from acting. Adults' reaction times reliably reflected the agent's beliefs only when the agent was free to act on the ball and not when the agent was visibly constrained from acting. Furthermore, it was the agent's constrained action capabilities, rather than any perceptual novelty, that determined whether adult observers' reaction times reliably reflected the agent's beliefs. These findings signal that our motor system may underpin more of social cognition than previously imagined, and, in particular, that motor representations may underpin automatic false-belief tracking.