The twister was reported around 1:40 p.m. in Scotts Valley, about 30 miles south of San Jose, according to the National Weather Service.
After conducting a preliminary damage survey, the weather service rated the tornado as an EF-1 with estimated peak winds of 90 mph.
Several people were taken to the hospital with injuries, but there are no reported deaths, according to a press release from the Scotts Valley Police Department.
"Emergency medical teams are prioritizing those most in need of care, and we continue to monitor the situation closely," police said in the news release.
The tornado caused "significant damage" in several areas, police said.
Photos shared by police on social media showed multiple cars turned on their sides along the roadway and in a shopping center parking lot.
Police asked people to avoid the area impacted.
Earlier on Saturday, the National Weather Service issued San Francisco's first-ever tornado warning as a strong storm moved through the region.
Tornado Warning lifted for SF, Daly City and Broadmoor
The warning was issued at 5:52 a.m. and was canceled about 20 minutes later.
KGO-TV meteorologist Lisa Argen said the last warning closest to the area was for South San Francisco in the 1980s. There were reported power outages around the Bay Area.
KGO spoke with some Daly City residents, one of whom said conditions were "nasty outside."
ABC News contributed to this report.