Understanding how often individuals should move when foraging over patchy habitats is a central question in ecology. By combining optimality and functional response theories, we show analytically how the optimal movement rate varies with the average resource level (enrichment) and resource distribution (patch heterogeneity). We find that the type of functional response predicts the effect of enrichment in homogeneous habitats: enrichment should decrease movement for decelerating functional responses, but increase movement for accelerating responses. An intermediate resource level thus maximises movement for type-III responses. Counterintuitively, greater movement costs favour an increase in movement. In heterogeneous habitats predictions further depend on how enrichment alters the variance of resource distribution. Greater patch variance always increases the optimal rate of movement, except for type-IV functional responses. While the functional response is well established as a fundamental determinant of consumer–resource dynamics, our results indicate its importance extends to the understanding of individual movement strategies.