Firefighters were called around 4:30 am to the building on Kern Street and Van Ness Avenue.
When they arrived, they found a small fire burning on the fifth floor.
Fire officials said an ottoman caught fire, but the building's sprinkler system put out the flames.
Initially, everyone inside the building was evacuated while firefighters investigated.
Firefighters said water damaged three to four units in the building.
Those residents will need to be moved to other units in the building.
No one was hurt.
The cause of the fire is still under investigation.