Crews responded to Argyle Avenue near Kings Canyon Road and Clovis Avenue.
They found heavy smoke coming from the apartment units and flames in the building's attic.
More firefighters were called to help battle the flames.
Crews rescued one bedridden resident from one of the units. The person was taken to a local hospital for treatment for smoke inhalation.
All four of the units were damaged by smoke and water. Several people are now displaced.
Officials say one dog was killed in the fire.
The cause of the fire is under investigation.