Los Angeles County Fire Department officials responded to the crash near San Gabriel Dam at Mile Marker 21.67 shortly after 5 p.m.
Search-and-rescue crews worked to reach the crash site after a witness reported seeing the vehicle go over the side and catch fire.
California Highway Patrol officials later confirmed at least one fatality in the incident.
The crash sparked a blaze, which burned at least two acres, but the forward progress was quickly stopped by firefighters at the scene.
Highway 39 was expected to be closed from Morris Dam until Tuesday morning.