The fire was reported at 1:38 p.m. at a two-story apartment complex in the 5200 block of Clayton Road.
Fire Marshal Lewis Broschard said firefighters found the victim, a 35-year-old woman, in the living room area of the apartment where the fire started, unconscious and not breathing. They brought her outside and paramedics gave her CPR at the scene.
She was then taken to a hospital where she was listed in critical condition.
"Fire paramedics were able to get a pulse and blood pressure prior to leaving the scene," Broschard said.
The woman who was injured lives with a roommate in the unit where the fire started, Broschard said. The roommate was not home at the time.
He said it appears the apartment, which sustained significant damage, was equipped with working smoke detectors.
No other injuries were reported, and the cause of the fire remains under investigation.
Broschard said six to eight other apartments had water or smoke damage. A number of residents were displaced, but only one sought assistance from the American Red Cross, he said.