Three eyewitnesses tried to reach the van and rescue anyone inside while it was still only partly submerged, the San Francisco Chronicle reported. But it sank below the surface, leaving police divers to grope for 2 hours in water where visibility was close to zero.
Gordon Shyy, a police spokesman, said sonar was used to pinpoint the vehicle's location and the body was found at about 8 p.m.
The driver's identity was not released pending notification of the family.
Assistant Fire Chief Bob Postel said witnesses saw the van moving at 20 mph, a dangerous speed in a parking lot, just after 5 p.m. It went into the bay near the San Francisco Yacht Harbor.
Three people who attempted to reach the van while it was sinking had to be rescued themselves, police said. John Pollak, 13, who was playing catch with his father when the van went in, said the trio dived off a boat into the water and swam to the van.