The mental representation of one's body typically implies the continuity of its parts. Here, we used immersive virtual reality to explore whether mere observation of visual discontinuity between the hand and limb of an avatar could influence a person's sense of ownership of the virtual body (feeling of ownership, FO) and being the agent of its actions (vicarious agency, VA). In experiment 1, we tested whether placing different amounts of visual discontinuity between a virtual hand and limb differently modulate the perceived FO and VA. Participants passively observed from a first-person perspective four different versions of a virtual limb: (1) a full limb; a hand detached from the proximal part of the limb because of deletion of (2) the wrist; (3) the wrist and forearm; (4) and the wrist, forearm and elbow. After observing the static or moving virtual limb, participants reported their feeling of ownership (FO) and vicarious agency (VA) over the hand. We found that even a small visual discontinuity between the virtual hand and arm significantly decreased participants' FO over the hand during observation of the static limb. Moreover, in the same condition, we found that passive observation of the avatar's actions induced a decrease in both FO and VA. We replicated the same results in a second study (experiment 2) where we investigated the modulation of FO and VA by comparing the visual body discontinuity with a condition in which the virtual limb was partially occluded. Our data show that mere observation of limb discontinuity can change a person's ownership and agency over a virtual body observed from a first-person perspective, even in the absence of any multisensory stimulation of the real body. These results shed new light on the role of body visual continuity in modulating self-awareness and agency in immersive virtual reality.