Tactile perception is inhibited during movement execution, a phenomenon known as tactile suppression. Here, we investigated whether the type of movement determines whether or not this form of sensory suppression occurs. Participants performed simple reaching or exploratory movements. Tactile discrimination thresholds were calculated for vibratory stimuli delivered to participants' wrists while executing the movement, and while at rest (a tactile discrimination task, TD). We also measured discrimination performance in a same vs. different task for the explored materials during the execution of the different movements (a surface discrimination task, SD). The TD and SD tasks could either be performed singly or together, both under active movement and passive conditions. Consistent with previous results, tactile thresholds measured at rest were significantly lower than those measured during both active movement and passive touch (that is, tactile suppression was observed). Moreover, SD performance was significantly better under conditions of single-tasking, active movements, as well as exploratory movements, as compared to conditions of dual-tasking, passive movements, and reaching movements, respectively. Therefore, the present results demonstrate that when active hand movements are made with the purpose of gaining information about the surface properties of different materials an enhanced perceptual performance is observed. As such, it would appear that tactile suppression occurs for irrelevant tactual features during both reaching and exploratory movements, but not for those task-relevant features that result from action execution during tactile exploration. Taken together, then, these results support a context-dependent modulation of tactile suppression during movement execution.