The primate visual system has an exquisite ability to discriminate partially occluded shapes. Recent electrophysiological recordings suggest that response dynamics in intermediate visual cortical area V4, shaped by feedback from prefrontal cortex (PFC), may play a key role. To probe the algorithms that may underlie these findings, we build and test a model of V4 and PFC interactions based on a hierarchical predictive coding framework. We propose that probabilistic inference occurs in two steps. Initially, V4 responses are driven solely by bottom-up sensory input and are thus strongly influenced by the level of occlusion. After a delay, V4 responses combine both feedforward input and feedback signals from the PFC; the latter reflect predictions made by PFC about the visual stimulus underlying V4 activity. We find that this model captures key features of V4 and PFC dynamics observed in experiments. Specifically, PFC responses are strongest for occluded stimuli and delayed responses in V4 are less sensitive to occlusion, supporting our hypothesis that the feedback signals from PFC underlie robust discrimination of occluded shapes. Thus, our study proposes that area V4 and PFC participate in hierarchical inference, with feedback signals encoding top-down predictions about occluded shapes.