Fire Department spokeswoman Mindy Talmadge said at least 16 people living above the Matcha sushi restaurant at 915 Kearny St. were being assisted by the Red Cross to find temporary homes.
The fire was reported just before 8:30 a.m. and was brought under control about an hour later. It began in the rear of the sushi restaurant.
"It appears to have started in the kitchen area," Talmadge said.
The fire then spread upstairs into the residential part of the building, damaging seven or eight units. It also spread to a neighboring liquor store and a cocktail lounge.
Talmadge said all of the residents escaped from the building without injury.
The restaurant opened only about a week ago, according to Talmadge.
The cause of the fire is under investigation.