No injuries were reported and there was no sign of fuel leaking, but part of the Overseas Reymar's outer hull appeared crushed, the Los Angeles Times reported.
U.S. Coast Guard Lt. Cmdr. Shawn Lansing said the tanker struck the tower just west of Yerba Buena Island as it headed to sea.
The ship was being inspected and the ship's unidentified pilot and captain were to undergo drug and alcohol testing, which is standard protocol under federal law, Lansing said.
"Initial findings are that there is not any spill or discharge of product into the water," Lansing said. "Everyone on the vessel is safe."
An inspection of the bridge revealed a portion of one footing's wood-and-plastic fender was in need of repair.
"This is basically a scrape for the Bay Bridge," state Transportation Department spokesman Bart Ney said. "The fender system worked as designed."