Tactile sensitivity on a moving limb is reduced during movement. This phenomenon, known as tactile suppression, is attributed to internal forward models in which predictions of upcoming movement consequences are used to down-regulate actual sensory feedback caused by the movement. Moreover, successful movement control requires the use of incoming sensory feedback. Suppression is therefore modulated by feedback relevancy. An open question is whether the goal, i.e. movement’s anticipated future consequences, modulates how predictive and feedback signals are utilized. For example, feedback signals may become more relevant during avoidance than approach behaviors, as erroneous avoidance can be more detrimental than erroneous approach. Here, we examined tactile sensitivity on a moving hand while participants approached or avoided a stimulus. Additionally, we tested whether movement type (arm extension or flexion), previously shown to facilitate behavioral tendencies of approach and avoidance, modulate tactile sensitivity when these goals were reached by both types of movement. Participants flexed and extended their arm towards a positive or away from a negative stimulus in virtual reality (VR). We probed tactile suppression by presenting brief vibrations during movement through the VR-controller. Participants then responded whether they detected this vibration or not. Detection thresholds were significantly larger in all movement conditions compared to when the arm was at rest, indicating tactile suppression. Importantly, detection thresholds were larger in the flexed compared to the extended arm, independent of the movement goal. These results suggest modulation of tactile sensitivity for movements towards the body, independent of the goal to avoid or approach.