The medial temporal lobe is critical for both spatial navigation and memory. Although single neurons in the medial temporal lobe activate to represent locations in the environment during navigation, how this spatial tuning relates to memory for events involving those locations remains unclear. We examined memory-related changes in spatial tuning by recording single-neuron activity from neurosurgical patients performing a virtual-reality object-location memory task. We identified 'memory-trace cells' with activity that was spatially tuned to the retrieved location of the specific object that participants were cued to remember. Memory-trace cells in the entorhinal cortex, in particular, encoded discriminable representations of different memories through a memory-specific rate code. These findings indicate that single neurons in the human entorhinal cortex change their spatial tuning to target relevant memories for retrieval.