The girl, Maria, was hit in the driveway of the family's home Wednesday afternoon by a Toyota Land Cruiser driven by her teenage brother, said Laura McPherson, a spokeswoman for the Tennessee Highway Patrol.
The brother, whose name and exact age weren't available, apparently did not see the girl, McPherson said. No charges are expected.
"It looks like a tragic accident," she said.
Several family members witnessed the accident, which happened in Williamson County just south of Nashville. The girl died later at Vanderbilt University Medical Center in Nashville, hospital spokeswoman Laurie Holloway said.
Prayers are for the Chapman family at this time.