A striking example of the constructive nature of visual perception is how the human visual system completes contours of occluded objects. To date, it is unclear whether perceptual completion emerges during early stages of visual processing or whether higher-level mechanisms are necessary. To answer this question, we used transcranial magnetic stimulation to disrupt signaling in V1/V2 and in the lateral occipital (LO) area at different moments in time while participants performed a discrimination task involving a Kanizsa-type illusory figure. Results show that both V1/V2 and higher-level visual area LO are critically involved in perceptual completion. However, these areas seem to be involved in an inverse hierarchical fashion, in which the critical time window for V1/V2 follows that for LO. These results are in line with the growing evidence that feedback to V1/V2 contributes to perceptual completion.