The crash happened around 1:45 p.m. Wednesday and left the bridge closed for about three hours.
It appears the crash involved a van and the dump truck, with the dump truck then leaving the scene.
Police say the dump truck was coming into New Jersey and loaded with stone.
In a photo released by police, the truck has a purple cab and appears to have NJ tags.
Anyone with information on the identity of the vehicle's driver is asked to contact Burlington County Bridge Commission Police Department at 856-829-3002.
There is no word yet on any injuries as a result of the crash.