Heavy smoke was visible, coming from the top floor of the building in the 6600-block of North Newgard as firefighters worked to stop the fire from spreading. The fire department says 10 of the building's 20 units were damaged.
One firefighter was taken to the hospital with minor injuries.
No residents were injured, although some have been left temporarily homeless by the fire.
"When I looked out, all I saw were flames coming toward me. In my pajamas, I ran out and got dressed in the hallway, banged on the doors, rang all the doorbells and waited outside," said fire victim Helen Zamora.
A fire department spokesperson said the fire appeared to have started in a stairwell. The cause is under investigation.