Firefighters responded at about 6:20 a.m. to a report of smoke at Piazza's Market, located at 3970 Middlefield Road.
They determined the smoke was caused by a refrigerant leak in the mechanical room in the back of the business, according to the fire department.
All occupants of the business were evacuated as a refrigerator technician worked to stop the leak.
Piazza's Market will remain closed until a health inspector deems it safe to reopen.
Neighboring businesses were not affected and no one was harmed, the fire department said.