It happened in the 4700 block of New Hope Road.
Video from Chopper 11 HD showed that much of the damage appeared to be to the roof of the building.
No injuries were reported but fire officials say 12 units are uninhabitable.
In total, about 25 percent of the building was damaged.
Residents said they were understandably worried.
"I don't know if anybody got hurt.. any kids in there, anything," said resident Angela Brooks. "It's like it spread from one building to four. Very nervous because it could have happened to our apartment. We could have went through the same thing."
Authorities said it was accidental but have not commented on the exact cause.