Perception of depth is a fundamental challenge for the visual system, particularly for observers moving through their environment. The brain makes use of multiple visual cues to reconstruct the three-dimensional structure of a scene. One potent cue, motion parallax, frequently arises during translation of the observer because the images of objects at different distances move across the retina with different velocities. Human psychophysical studies have demonstrated that motion parallax can be a powerful depth cue, and motion parallax seems to be heavily exploited by animal species that lack highly developed binocular vision. However, little is known about the neural mechanisms that underlie this capacity. Here we show, by using a virtual-reality system to translate macaque monkeys (Macaca mulatta) while they viewed motion parallax displays that simulated objects at different depths, that many neurons in the middle temporal area (area MT) signal the sign of depth (near versus far) from motion parallax in the absence of other depth cues. To achieve this, neurons must combine visual motion with extra-retinal (non-visual) signals related to the animal's movement. Our findings suggest a new neural substrate for depth perception and demonstrate a robust interaction of visual and non-visual cues in area MT. Combined with previous studies that implicate area MT in depth perception based on binocular disparities, our results suggest that area MT contains a more general representation of three-dimensional space that makes use of multiple cues.