Brownsville police say the accident happened Wednesday night at the city's new La Plaza terminal.
Investigators say the driver had parked the bus and gotten out when the vehicle began rolling. He was struck while attempting to stop the bus.
Sgt. Albert de la Rosa says police will review surveillance video to try to determine how the accident happened. The driver was dead at the scene.
Details were not immediately available on the route or whether passengers were on board.
The $31 million new main bus terminal opened in April. The complex at the Brownsville Multimodal Terminal is near the Gateway International Bridge to Mexico.