Speakers convey meaning not only through words, but also through gestures. Although children are exposed to co-speech gestures from birth, we do not know how the developing brain comes to connect meaning conveyed in gesture with speech. We used functional magnetic resonance imaging (fMRI) to address this question and scanned 8- to 11-year-old children and adults listening to stories accompanied by hand movements, either meaningful co-speech gestures or meaningless self-adaptors. When listening to stories accompanied by both types of hand movement, both children and adults recruited inferior frontal, inferior parietal, and posterior temporal brain regions known to be involved in processing language not accompanied by hand movements. There were, however, age-related differences in activity in posterior superior temporal sulcus (STSp), inferior frontal gyrus, "pars triangularis" (IFGTr), and posterior middle temporal gyrus (MTGp) regions previously implicated in processing gesture. Both children and adults showed sensitivity to the meaning of hand movements in IFGTr and MTGp, but in different ways. Finally, we found that hand movement meaning modulates interactions between STSp and other posterior temporal and inferior parietal regions for adults, but not for children. These results shed light on the developing neural substrate for understanding meaning contributed by co-speech gesture.