At least two vehicles - a car and a small truck - either were struck by or ran into the fallen rod, said California Highway Patrol Officer Peter Van Eckhardt. No injuries were reported.
The California Department of Transportation said Tuesday that it will remain closed indefinitely.
A spokesman for the Bay Area Rapid Transit District, meanwhile, said extra trains would run during the morning commute. The rod that fell Tuesday was erected last month during an emergency repair job. It was holding in place a saddle-like cap that had been installed over a cracked link discovered over the Labor Day weekend.
When the rod apparently snapped at about 5:30 p.m., it brought down with it a steel patch roughly 3 feet long, authorities said.
"If you look at the totality of the circumstances - you've got the 5:30 commute, you have a 5,000-pound piece of steel falling out of the sky. We are so fortunate that no one was injured or killed," CHP Sgt. Trent Cross told KTVU-TV.
Officers managed to clear the Oakland-bound traffic from the lower deck of the bridge by 8 p.m. but were still clearing cars from the few remaining open lanes of the upper deck an hour later, he said.
The bridge was closed last month over the holiday weekend for long-planned earthquake safety upgrades. When the crack was discovered, state transportation officials initially feared it would prevent them from reopening the span in time for the start of the work week. But the unexpected work only ended up taking a few extra hours.
California Department of Transportation, or Caltrans, officials had nothing to say Tuesday about what might have caused the failure. The department issued a brief statement saying only that "structural engineers and inspectors are onsite to assess the damage and will make a determination as to how long repairs will take.
"At this time, the bridge is closed until further notice," the statement said.
Abolhassan Astaneh-Asl, a civil engineering professor at the University of California, Berkeley, who has spent 20 years studying the Bay Bridge, called the initial crack a "warning sign" of potentially bigger safety issues with the bridge.
"The repair they were doing was really a Band-Aid," said Astaneh-Asl, who criticized Caltrans at the time for rushing to reopen the bridge.
Astaneh-Asl said the failure of the repair job demonstrates the need for a longer-term solution. The bridge's age and design make it susceptible to collapse, especially if commercial tractor-trailers are allowed to continue using it, he said.
"I think Caltrans is putting public relations ahead of public safety," he said.