Sense of agency (SoA), a crucial ability for everyday motor tasks, describes the feeling of being in control of self-generated movements. When internal predictions of motor actions do not match the final outcome, severe irritation and a diminished feeling of control can occur. Hence, this study seeks to gain a deeper understanding of the underlying neural mechanisms of SoA. An MRI-compatible soft exoskeleton on the right hand was used to examine the SoA during different grasping mechanisms in a functional magnetic resonance imaging (fMRI) task. Moreover, subjective SoA ratings were collected. The paradigm included active and passive task blocks, in which participants either actively grasped without any exoskeleton assistance or the exoskeleton fully executed the grasp while participants did not engage in any motor actions. In addition, an assisted condition, in which both the participant and the exoskeleton grasped simultaneously, was included. The study sample consisted of 25 healthy participants. Low subjective SoA ratings were found to be related to the passive condition, whereas high subjective SoA ratings were related to the active condition, with ratings for the assisted condition lying in between. Using an FWE-corrected alpha of 0.05, the active condition, compared to both the passive and assisted conditions, showed significant cerebellar activation, while the passive condition, compared to the active and assisted conditions, showed an angular gyrus activation. These results underline previous research findings associating motor area activation with high SoA and angular gyrus activation with low SoA.