Communities in South Dakota have also seen piles of snow on Tuesday with some seeing 18 inches of snow, AccuWeather said.
Three of the tornadoes touched down in Tarrant County, one in Wise County and one west of Paris, Texas in Lamar County.
"Line continues to move east producing isolated tornadoes, damaging winds, and hail up to quarter size," the Fort Worth office tweeted.
In Grapevine, 20 miles northwest of Dallas, at least five people were injured, and a Sam's Club, a Walmart and the Grapevine Mills Mall were shut down due to damage, police said. Several other businesses in the area also were damaged, police said in a Facebook post.
Emergency management officials in Dallas warned wind gusts could reach 70 mph and that hail was possible. Dallas-Fort Worth Airport briefly activated a "shelter in place" program.
"We ask that you move away from windows & exteriors," airport authorities said in a Tuesday morning tweet. "Shelter in enclosed spaces if you are at the airport. Please do not travel to the airport until the tornado warning is deactivated."
The alert was later cleared by the National Weather Service, but the airport urged travelers to "please check the weather in your area before traveling to the airport, and check with your airline for the latest on your flight status."
Meanwhile, at least two people were reported injured in Decatur, Texas, about 70 miles northwest of Dallas. One person was hurt when wind overturned their vehicle, and another in a separate vehicle was hurt by flying debris, the county's emergency management office said. One person was taken to the hospital and the other was treated at the scene.
Additionally, numerous homes and businesses were damaged due to the severe weather that hit east of Paradise and south of Decatur in Wise County, according to CNN.