The fire was reported shortly after 5:15 a.m. at the Terrace Apartments, a four-story, 75-unit apartment building at 926 Woodside Road.
Redwood City Fire Marshal Jim Palisi said the fire was controlled shortly before 9 a.m. but that crews remained at the scene around 11 a.m. putting out hotspots.
Four adults were hurt in the fire and were taken to hospitals, Palisi said. Two suffered moderate injuries and two suffered minor injuries.
He said the rescue effort was hectic but ultimately successful, with some people escaping the building on their own and others helped out by fire crews. He said some residents climbed over balconies to get out.
The most significant damage was to the fourth floor, where the blaze appears to have started, Palisi said.
Late this morning, Woodside Road remained closed between Massachusetts Avenue and Gordon Street.
The American Red Cross has set up an evacuation center at the Red Morton Community Center at 1120 Roosevelt Ave. to assist those displaced, spokeswoman Cynthia Shaw said.
Shaw said breakfast was served to dozens of evacuated residents. Other resources will be provided at the center throughout the day.
She said residents with pets should stop by the center to be connected with partner agencies that are helping pet owners.
The building is managed by Terrace Associates, Inc., which has properties throughout the Peninsula and South Bay region.
This morning's fire came several months after a fatal six-alarm fire burned at an apartment building just down the road.
That fire started at about 1:45 a.m. on July 7 at the Hallmark House Apartments, a 72-unit building at 531 Woodside Road, about half a mile from the Terrace Apartments.
One person was killed in that blaze and about 17 others were injured.