High winds and twisters also caused damage in Arkansas, Indiana and Kentucky.
Local emergency officials reported 15 deaths in west Tennessee's Dyer County, and the number of fatalities could rise, said Kurt Pickering, spokesman for the Tennessee Emergency Management Agency. He added that the full extent of the damage won't be known until the sun comes up.
A staff member at the Dyer County sheriff's office said they are "still trying to get to the injured people." She told The Tennessean newspaper the situation is "bad."
The storms also spawned at least six tornadoes and dropped softball-sized hail in northeast Arkansas.
In Indiana, thousands of concertgoers scrambled for cover as a possible twister passed through downtown Indianapolis.
In Missouri, strong winds were blamed for the deaths of at least two people. A 42-year-old man was killed when straight-line winds knocked over his mobile home near Circle City, Stoddard County Sheriff Carl Hefner said.
Another man was killed when a tree fell on him as he walked along a trail in Castlewood State Park near Ballwin in St. Louis County, a spokeswoman for St. Louis County police told the St. Louis Post-Dispatch.
In Illinois, a man was killed when a clothing store in Fairview Heights, east of St. Louis, collapsed in high winds, police Capt. Nick Gailius said.
Emergency crews were searching the rubble for any additional victims, their progress slowed by a gas leak, Gailius said. Others were injured in the collapse, he said.
In Tennessee, the National Weather Service reported that tornadoes were spotted in five counties in Tennessee's northwest corner, and officials said the storms caused extensive damage to buildings.