The California Highway Patrol said the crash was reported at Chicano Park shortly after 3:30 PM (local time) yesterday.
The city's Fire-Rescue Department said four people were declared dead at the scene.
Spokesman Lee Swanson said eight people were injured: four of them suffered major traumas and the other four had minor injuries. He said several more were evaluated by medics at the park.
The cause of the crash is under investigation and both sides of the bridge are closed to traffic.