Firefighters were called to the complex on Weldon Avenue and Fresno Street around 7:15am.
Fire crews arrived to find flames coming from the roof of the building. The fire destroyed at least one apartment unit.
PG&E will cut the power to the building, leaving residents in the 12 apartment units temporarily without a home. The Red Cross was helping them find a place to stay.
No one was injured, but firefighters were checking to see if any of the people suffered smoke inhalation.
The cause of the fire is under investigation.