Scott Bradley, a police chief at Van Buren County in Arkansas, told local media that three members of the same family were killed in his area.
“The house they were in sustained a direct hit, was totally destroyed,” he said.
Bradley also said that some 28 homes had been completely destroyed and 10 others damaged.
The tornadoes struck around 8.30am just as people were preparing to leave for work and school in the south-central state.
Bradley said that clean-up operations had already begun.
Greg Carbin, a meteorologist for the national Storm Prediction Centre in Norman, Oklahoma, said as many as 25 tornadoes may have cut through stretches of Oklahoma, Arkansas, eastern Kansas and western Missouri.
In Siloam Springs, southern Arkansas, a 15-year-old girl was killed while sleeping when a tree fell on her room when the first wave of tornadoes struck at about 4.30am, local media reported, citing police.
Her 10-year old brother, sleeping in the same room, was slightly injured and hospitalised.
According to local emergency services, a father and son were also reported killed when a tornado hit their home in nearby Conway County, and at least one person was killed in the town of Hensley.
The storms damaged property, uprooted trees and blew out electric services to thousands of homes and businesses across Arkansas.
In Texas, they appeared to touch down in at least three eastern towns, uprooting trees, flipping cars and tearing down power lines.
In Oklahoma, at least three tornadoes hit central and northern towns, including one in Osage county near Tulsa that was an estimated 100 yards wide, but no serious injuries were reported there.
A home was destroyed and about a dozen others were damaged in northeastern Oklahoma, while a hotel under construction near Tulsa was ruined.