Kathy Jividen, a spokeswoman for the Hood County, Texas, sheriff's office said there were "multiple fatalities" in the wake of the storm.
Hood County Judge Darrell Cockerham said there were reports of homes being flattened with people inside.
City officials were sending school buses to affected neighborhoods to help with evacuations.
The National Weather Service warned that a mile-wide tornado reported by spotters had shifted its track and was moving "right at the city of Cleburne," a community of about 15,000 people in north Texas.
"If you are in its path ... take cover immediately to protect your life," the weather service alert said.
The National Weather Service also said 32 counties in Texas and four in Oklahoma were under a tornado watch until 1 a.m. CT.
Granbury is about 40 miles southwest of Fort Worth.