To achieve stable and precise movement execution, the sensorimotor system integrates exafferent sensory signals originating from interactions with the external world and reafferent signals caused by our own movements. This barrage of sensory information is regulated such that behaviorally relevant signals are boosted at the expense of irrelevant ones. For example, sensitivity to touch is reduced during movement – when cutaneous signals caused by skin stretch are expected and uninteresting – a phenomenon reflected in a decreased cutaneous responsiveness in thalamus and cortex. Some evidence suggests that movement gating of touch may originate from the cuneate nucleus (CN), the first recipient of signals from tactile nerve fibers along the dorsal column-medial lemniscus pathway. To test this possibility, we intermittently delivered mechanical pulses to the receptive fields (RFs) of identified cutaneous CN neurons as monkeys performed a reach-to-grasp task. As predicted, we found that the cutaneous responses of individual CN neurons were reduced during movement. In contrast, cutaneous signals from neurons with RFs on the hand were enhanced during reach. We conclude that tactile signals are already modulated in the first processing stage along the somatosensory neuraxis. Furthermore, the sign and magnitude of this modulation depends on the behavioral relevance of the sensory signals.