The injured include the taxi driver, as well as two people who were standing on the sidewalk. The crash happened around 3 p.m., not far from the Montgomery BART station at Market Street near Sutter Street.
Witnesses say the yellow cab was flying down Market Street when it went over the curb at Sutter Street and crashed into an advertising kiosk and a shoeshine stand where two people were working.
PHOTOS: Taxi crashes into pedestrians in SF Financial District
"I just heard a crash, but what I did see was the old man flying up in the air, like something out of a movie, like something unbelievable. He laid down of the ground and he wasn't moving," said Susan Marie Giammona, a witness.
Another man in his 40s she says was buried in debris. The cab driver stumbled out of the taxi and collapsed on the sidewalk.
"There are three people who are facing life-threatening injuries from this collision. Two of them were at the shoe shine stand and one was the driver. They have all been transported to local trauma centers," said San Francisco police Officer Grace Gatapandan.
Giammona was only 4 feet away from the crash in her jewelry stand. She said people stopped to help, calling them the angels of San Francisco, as she called 911.
An investigation into the cause of the crash is underway. The right lane of westbound Market Street is only open to delivery trucks and taxis.
"I see them going down here 60 miles an hour, sometimes more, to get to their next destination. And this is what happens. He was going very fast," Giammona said.
Three ambulances and three fire engines responded within six minutes. A crowd of people stood around the accident scene Tuesday afternoon in disbelief saying they pass the shoe shine stand every day and see the stand that's been there for at least 20 years. They said they are hoping and praying everyone pulls through.
SUTTER AT SANSOME MAJOR COLLISION 3 CRITICAL AVOID AREA pic.twitter.com/0lBhSBq3QC— San Francisco Fire (@sffdpio) August 23, 2016
SUTTER SANSOME UPDATE 3 critical adults VEH into pedestrians AVOID AREA pic.twitter.com/YmpCx6sYVg— San Francisco Fire (@sffdpio) August 23, 2016