Little is known about how animals use tactile sensation to detect important objects and remember their location in a world-based coordinate system. Here, we hypothesized that retrosplenial cortex (RSC), a key network for contextual memory and spatial navigation, represents the location of objects based on tactile sensation. We studied mice that palpate objects with their whiskers while running on a treadmill in a tactile virtual reality in darkness. Using two-photon Ca2+ imaging, we discovered a population of neurons in agranular RSC that signal the location of tactile objects. Tactile object location responses do not simply reflect the sensory stimulus. Instead, they are highly task- and context-dependent and often predict the upcoming object before it is within reach. In addition, most tactile object location neurons also maintain a memory trace of the object's location. These data show that RSC encodes the location and arrangement of tactile objects in a spatial reference frame.