In the last few years, research on the detection of AI-generated videos has focused exclusively on detecting facial manipulations known as deepfakes. Much less attention has been paid to the detection of artificial non-facial fake videos. In this paper, we address a new forensic task, namely, the detection of fake videos of human body reenactment. To this purpose, we consider videos generated by the “Everybody Dance Now” framework. To accomplish our task, we have constructed and released a novel dataset of fake videos of this kind, referred to as FakeDance dataset. Additionally, we propose two forgery detectors to study the detectability of FakeDance kind of videos. The first one exploits spatial–temporal clues of a given video by means of hand-crafted descriptors, whereas the second detector is an end-to-end detector based on Convolutional Neural Networks (CNNs) trained on purpose. Both detectors have their peculiarities and strengths, working well in different operative scenarios. We believe that our proposed dataset together with the two detectors will contribute to the research on the detection of non-facial fake videos generated by means of AI.