KFOR-TV, Oklahoma City, reported the woman and child were killed while traveling on Interstate 40 between El Reno and Yukon.
"We try to tell people not to drive into the storm," Betsy Randolph of the Oklahoma Highway Patrol told the TV station. "This could have been a situation where there was little to no notice or warning. It's so gut-wrenching and heartbreaking."
Randolph confirmed there were other multiple crashes in Mustang, El Reno, Yukon, Oklahoma City, Moore and Norman, where strong winds or another tornado may have struck, KFOR-TV said.
The Highway Patrol blocked I-40 because of the storm and authorities said Highway 9 was gridlocked with cars trying to get out of the storm's path.
KOCO-TV, Oklahoma City, reported the Highway Patrol said there were motorists injured and others were missing.
KOTV-DT, Oklahoma City, reported a semi-trailer truck and multiple cars had been flipped over, causing multiple injuries.
Authorities told people to stay off the roads and seek shelter immediately.
NBC News reported the funnel cloud -- up to a mile wide at one point -- touched down near El Reno, just west of Oklahoma City.
Extensive damage was reported in the El Reno and Yukon suburbs, KFOR-TV reported. Power was knocked out to about 55,000 customers.
Weather Channel meteorologist Mike Bettes said the tornado tossed a vehicle used by the broadcaster's personnel about 200 yards. Bettes and his crew escaped injury, NBC said.
The storm came a week after a tornado killed 24 people in Moore, another Oklahoma City suburb.
KOTV-DT reported multiple tornadoes were reported across central Oklahoma, with strong storms hurling hail stones the size of baseballs in some areas.
Tornado warnings were widespread in Oklahoma and Missouri. The National Weather Service declared tornado watches over large sections of Oklahoma, Kansas and Missouri through late Friday.
Severe storm warnings were issued from Minnesota and Michigan to Arkansas.
Friday's storms follow severe weather overnight in Arkansas where tornadoes were to blame for the deaths of two people and injuries to nine others.