<p>Much of human memory takes the form of cognitive graphs that allow us to relate and generalize knowledge. The influence of structured memory in the motor system is less clear. Here we examine how structured memory representations influence action selection when responses are retrieved from newly learned, hierarchical visuomotor maps. Human participants (<i>N</i> = 182) learned visuomotor mappings with (or without) an imposed latent structure that linked visual stimulus features (for example, colour or shape) to intuitive motor distinctions, such as hands and pairs of fingers. In participants who learned structured visuomotor mappings, transitional response times indicated that retrieving the correct response from memory invoked the ‘traversal’ of a structured mental graph. Forced-response experiments revealed similar computations within individual trials. Moreover, graph-like representations persisted even after multiple days of practice with the visuomotor mappings. Our results point to direct links between internal computations over structured memory representations and the preparation of movements.</p>