Durham fire officials said the department responded to the 1700 block of East Cornwallis Road just before 8 p.m.
Two residents escaped from the blaze by climbing onto a small roof over the door and jumping to the ground. One occupant sustained a leg injury and was hospitalized.
Crews were able to get the blaze under control in around five minutes but there was extensive smoke and fire damage to the first and second floor.
The Durham Fire Department said the cause was unattended cooking.
No other units or occupants were affected and the two residents involved are being assisted by the American Red Cross.
See breaking news? Tell us about it here.