The Pamban road bridge is built across the sea connecting Rameswaram island with the mainland.
Police said the van driver had swerved the vehicle to avoid hitting coconut tree logs which fell from a tractor and rolled down after the rope holding them together snapped.
The van jumped the platform of the bridge, hit the railings and stopped.
Traffic was affected for half an hour following the accident.
The driver of the van and the tractor have been arrested, police said.