The Oklahoman reported the twister hit the ground about 4 p.m. and hopscotched for about 8 miles
Norman Regional Hospital spokeswoman Kelly Wells said at least 10 victims were treated for scrapes, bruises and other minor injuries.
"It is surprising you don't have more injured with the time of day, about 4:02 [p.m.]," Deputy Fire Chief Jim Bailey told the newspaper. "Norman is a busy town. There were a lot of people out driving around, and we had very little notification."
Philip DeFatta said he took cover in his body shop and heard the medical records building next door get hit.
"It's gone," he said. "The roof's gone. It's all over the place. The front wall is down. Part of it is in my building."
The tornado also knocked down power lines and trees.
The newspaper said there were unconfirmed reports of tornadoes in Altus, Cooperton and Carnegie.
The National Weather Service said more tornadoes and severe weather are possible Saturday.
Storms in California set off an estimated 3,000 lightning strikes, including one that hit an airliner before it landed safely in San Francisco Thursday, officials said.
Officials said a United Airlines flight that departed San Francisco International Airport for London was struck by a lightning bolt, then returned to the airport, KGO-TV, San Francisco reported.
No injuries were reported.
San Francisco Airport officials said 61 flights were canceled and some were delayed for several hours because of the storm.
Weather officials said 3,000 lightning strikes were reported statewide.
The Bay Area was rocked by heavy storms that lined up over the Pacific Ocean and carried heavy rains, winds, thunder and lightning, forecasters said.
The ground was so saturated in one neighborhood that a tree toppled over, blocking a street and knocking out power in the area, officials said.
The storm caused power outages affecting more than 3,700 people.
California could expect more soaking rains -- along with heavy snow in the mountain regions -- during the weekend, AccuWeather.com reported Friday.
"The storm will bring all the ingredients for thunderstorms with strong winds, hail, waterspouts and even a few tornadoes over portions of central and Southern California Friday," AccuWeather.com meteorologist Ken Clark said.
Clark said thunderstorms could knock down trees and power lines in some communities and people living in the mountains could see up to 2 feet of snow.
The system could trigger severe weather over the Plains states later in the weekend, AccuWeather.com said.