Traumatic brain injury (TBI) commonly results in cognitive and psychiatric problems. Cognitive impairments occur in approximately 30% of patients suffering from mild TBI (mTBI), and correlational evidence from clinical studies indicates that substance abuse may be increased following mTBI. However, understanding the lasting cognitive and psychiatric problems stemming from mTBI is difficult in clinical settings where pre-injury assessment may not be possible or accurate. Therefore, we used a previously characterized blast model of mTBI (bTBI) to examine cognitive- and addiction-related outcomes. We previously demonstrated that this model leads to bilateral damage of the medial prefrontal cortex (mPFC), a region critical for cognitive function and addiction. Rats were exposed to bTBI and tested in operant learning tasks several weeks after injury. bTBI rats made more errors during acquisition of a cue discrimination task compared to sham treated rats. Surprisingly, we observed no differences between groups in set shifting and delayed matching to sample, tasks known to require the mPFC. Separate rats performed cocaine self-administration. No group differences were found in intake or extinction, and only subtle differences were observed in drug-primed reinstatement 3–4 months after injury. These findings indicate that bTBI impairs acquisition of a visual discrimination task and that bTBI does not significantly increase the ability of cocaine exposure to trigger drug seeking.