The gunman was also injured in the incident outside the Jefferson County Courthouse in Beaumont. Officials said the suspect, who was not identified, was taken to an area hospital.
The motive behind the shooting remains unclear, but investigators say the suspect was a defendant in a child sex case and was going to court with his family when he started shooting.
ABC News reports the suspect shot his ex-wife and daughter, and escalated the damage by running over his daughter with his truck.
The suspect then drove three to four blocks away from the courthouse before he abandoned his truck in the middle of the street, police said. A witness said he saw police shooting at a truck and recalled hearing at least 30 shots total.
Beaumont is about 80 miles east of Houston.
ABC News and The Associated Press contributed to this report.