Flames rose from an apartment building at 1656 Powell St. near Union St. at 9:30 a.m. Sunday.
Firefighters were able to knock it down in 40 minutes, but the fire left its mark.
"We have at least 12 units with significant damage, so we're looking at least 12 units displaced with potentially more," said SFFD Division Chief Lorrie Kalos. "Once the people who don't have as much damage go in and see the conditions, they may choose not to come back home."
The fire began on the top floor in the rear of the building. Businesses on the bottom floor also suffered water damage.
There were no reports of injuries.