Two cars were involved in a road accident on the Uppingham Road near Caldecott on Friday night.
A silver Rover 25 was left on its roof and the other vehicle left the scene before emergency services arrived.
Fire crews from Uppingham and Corby attended the incident on the A6003 at 7pm and made the scene safe.
No one was trapped.
The male driver of Rover was taken to Kettering Hospital by ambulance as a precaution.
Police are appealing for anyone who may have witnessed the accident and have information about the driver who failed to stop, to contact them on 101.