Crews responded about 4:40 p.m. to the 23200 block of 88th Avenue South to find smoke and flames coming from a third-story apartment, according to Kent Fire.
The resident of the unit was taken to a local hospital for injuries that were not life-threatening, and no other occupants of the building were hurt, firefighters said.
One cat in the apartment died and two others are missing.
Damage to two other apartments displaced the residents of those units.
Managers of the complex were working to find them housing, Kent Fire officials said.
Investigators are still working to determine the cause of the blaze.