Certain regions of the human brain are activated both during action execution and action observation. This so-called ‘mirror neuron system’ has been proposed to enable an observer to understand an action through a process of internal motor simulation. Although there has been much speculation about the existence of such a system from early in life, to date there is little direct evidence that young infants recruit brain areas involved in action production during action observation. To address this question, we identified the individual frequency range in which sensorimotor alpha-band activity was attenuated in nine-month-old infants' electroencephalographs (EEGs) during elicited reaching for objects, and measured whether activity in this frequency range was also modulated by observing others' actions. We found that observing a grasping action resulted in motor activation in the infant brain, but that this activity began prior to observation of the action, once it could be anticipated. These results demonstrate not only that infants, like adults, display overlapping neural activity during execution and observation of actions, but that this activation, rather than being directly induced by the visual input, is driven by infants' understanding of a forthcoming action. These results provide support for theories implicating the motor system in action prediction.