Summary Mammals use distances and directions from local objects to calculate trajectories during navigation but how such vectorial operations are implemented in neural representations of space has not been determined. Here we show in freely moving mice that a population of neurons in the medial entorhinal cortex (MEC) responds specifically when the animal is at a given distance and direction from a spatially confined object. These ‘object-vector cells’ are tuned similarly to a spectrum of discrete objects, irrespective of their location in the test arena. The vector relationships are expressed from the outset in novel environments with novel objects. Object-vector cells are distinct from grid cells, which use a distal reference frame, but the cells exhibit some mixed selectivity with head-direction and border cells. Collectively, these observations show that object locations are integrated in metric representations of self-location, with specific subsets of MEC neurons encoding vector relationships to individual objects.