The extinction of delay fear conditioning relies on a neural circuit that has received much attention and is relatively well defined. Whether this established circuit also supports the extinction of more complex associations, however, is unclear. Trace fear conditioning is a better model of complex relational learning, yet the circuit that supports extinction of this memory has received very little attention. Recent research has indicated that trace fear extinction requires a different neural circuit than delay extinction; trace extinction requires the participation of the retrosplenial cortex, but not the amygdala, as noted in a previous study. Here, we tested the roles of the prelimbic and infralimbic regions of the medial prefrontal cortex in trace and delay fear extinction by blocking NMDA receptors during extinction learning. We found that the prelimbic cortex is necessary for trace, but not for delay fear extinction, whereas the infralimbic cortex is involved in both types of extinction. These results are consistent with the idea that trace fear associations require plasticity in multiple cortical areas for successful extinction. Further, the infralimbic cortex appears to play a role in extinction regardless of whether the animal was initially trained in trace or delay conditioning. Together, our results provide new information about how the neural circuits supporting trace and delay fear extinction differ.