During many natural behaviors the relevant sensory stimuli and motor outputs are difficult to quantify. Furthermore, the high dimensionality of the space of possible stimuli and movements compounds the problem of experimental control. Head fixation facilitates stimulus control and movement tracking, and can be combined with techniques for recording and manipulating neural activity. However, head-fixed mouse behaviors are typically trained through extensive instrumental conditioning. Here we present a whisker-based, tactile virtual reality system for head-fixed mice running on a spherical treadmill. Head-fixed mice displayed natural movements, including running and rhythmic whisking at 16 Hz. Whisking was centered on a set point that changed in concert with running so that more protracted whisking was correlated with faster running. During turning, whiskers moved in an asymmetric manner, with more retracted whisker positions in the turn direction and protracted whisker movements on the other side. Under some conditions, whisker movements were phase-coupled to strides. We simulated a virtual reality tactile corridor, consisting of two moveable walls controlled in a closed-loop by running speed and direction. Mice used their whiskers to track the walls of the winding corridor without training. Whisker curvature changes, which cause forces in the sensory follicles at the base of the whiskers, were tightly coupled to distance from the walls. Our behavioral system allows for precise control of sensorimotor variables during natural tactile navigation.