Officials identified the victim as Gretchen Urdang, 49.
Of those injured, one woman broke her leg when she jumped from a second-story window, authorities said. Four others suffered smoke inhalation and minor burns.
The fire started about 3:15 a.m. in a second-floor breezeway at Chesterfield Village Apartment, Assistant Fire Chief Bill Arington said.
The building was fully engulfed in flames when firefighters arrived, he said. It took about 90 minutes for the fire to be brought under control.
Investigators remained on the scene midday Wednesday, trying to determine the cause of the fire.
Eight of the units were destroyed, authorities said. A firewall stopped the blaze from spreading further, but the remaining units have smoke damage, Arington said. About 40 people were displaced by the fire.