It happened on I-45 N at Tiki Island Friday evening.
The Galveston County Sheriff's Office told Eyewitness News a man and a woman were in a vehicle with eight children.
Investigators said the driver was on a curved road and veered off at the Cloverleaf interchange into a field where the vehicle crashed.
Four children were rushed to the hospital and at least one of them suffered a broken leg.
None of the children were wearing seatbelts, according to authorities.
The man, who was driving the vehicle, is facing an intoxication assault charge. He was booked into the Galveston County Jail on a $50,000 bond, authorities said.