Residents of a five-unit residential building at 49 Birch St. reported the fire at 9:11 a.m., Redwood City fire Battalion Chief Steve Cavallero said.
The fire burned near the furnace in one of the units and was controlled at 9:42 a.m., Cavallero said.
No one was injured and residents of two of the five units were displaced.
The fire appears to be accidental and caused by a problem with the furnace, Cavallero said.
"We don't know if it was a maintenance issue or a malfunction with the furnace, but we do know it was an issue with the furnace," he said.
Cavallero is reminding residents to ensure that furnaces are properly maintained, including by checking the burners and cleaning the filters.