The crash happened just after 6 a.m. at Polk and Hayes streets.
A video captured by a surveillance camera at a nearby building shows a southbound pickup truck slamming into the right side of a westbound black SUV as both cars entered the intersection, which is controlled by a stoplight.
The impact crumpled the front end and passenger side of the SUV, which came to rest in an empty parking lot on the west side of Polk Street. The rear wheel was ripped off.
The pick-up truck, which was also badly damaged, came to rest on the southwest side of Hayes Street.
San Francisco Police Department Sgt. Troy Dangerfield said it is still unclear who was at fault.
Witnesses said an elderly woman appeared to have an arm injury and a young girl between 10 and 12 years old was among the wounded.
The crash shut down the intersection just as the morning commute was beginning.