Young primates have relatively large hands and feet for their body size, perhaps enhancing grasping ability. We test the hypothesis that selection for improved grasping ability is responsible for these scaling trends by examining the ontogeny of intrinsic hand and foot proportions in capuchin monkeys (Cebus albifrons and Sapajus apella). If selection for improved grasping ability is responsible for the observed patterns of hand and foot growth in primates, we predicted that fingers and toes would be longer early in life and proportionally decline with age. We measured the lengths of manual and pedal metapodials and phalanges in a mixed‐longitudinal radiographic sample. Bone lengths were (a) converted into phalangeal indices (summed non‐distal phalangeal length/metapodial length) to test for age‐related changes in intrinsic proportions and (b) fit to Gompertz models of growth to test for differences in the dynamics of phalangeal versus metapodial growth. Manual and pedal phalangeal indices nearly universally decreased with age in capuchin monkeys. Growth curve analyses revealed that metapodials generally grew at a faster rate, and for a longer duration, than corresponding phalanges. Our findings are consistent with the hypothesis that primates are under selection for increased grasping ability early in life. Relatively long digits may be functionally adaptive for growing capuchins, permitting a more secure grasp on both caregivers and arboreal supports, as well as facilitating early foraging. Additional studies of primates and other mammals, as well as tests of grasping performance, are required to fully evaluate the adaptive significance of primate hand and foot growth.