It was not immediately clear what caused the one-vehicle accident, said Li Hailiang, an employee at the Donghai Bridge Administration.
He said six people died on the scene and that an unspecified number of injured people were taken to a hospital.
The state broadcaster CCTV said more than 20 people were injured.
Donghai Bridge connects China's financial metropolis Shanghai with a deep-water port in the East China Sea. With a length of 32.5 kilometers (20.2 miles), it is one of the longest cross-sea bridges in the world.