The crew of the Overseas Reymar reported no loss of steering or propulsion, and initial investigations showed no water leaks from any of the ballast tanks, said Darrell Wilson, a spokesman for OSG.
"The ship's crew safely anchored the vessel and made all proper notifications to the authorities," Wilson said.
California Emergency Management Agency spokesman Jordan Scott said the structure of the bridge was fine. The tower of the bridge appeared to be fine from a distance, added California Department of Transportation spokesman Bart Ney.
"There is some damage to the vessel, but nothing that poses a danger to anybody," Scott said. "A fire boat is out there to make sure it stays that way, and it should."
The tanker docked west of Yerba Buena Island immediately following the crash, and the pilot was interviewed by the Coast Guard and the California Board of Pilot Commissioners for the Bays of San Francisco, San Pablo and Suisun, which regulates bar pilots.
The pilot has been a San Francisco bar pilot since 2005, Goodyear said. The association did not release his name.
State law requires a bar pilot to guide every large vessel — be it a luxury liner, a billionaire's yacht, aircraft carrier or cargo ship — in, out and around the San Francisco Bay.
The pilots' role came under intense scrutiny in the crash of the Cosco Busan. That ship's pilot, Capt. John Cota, served a 10-month prison sentence after pleading guilty to two misdemeanor charges.
The companies responsible for the Cosco Busan paid close to $60 million for the cleanup and in criminal fines.
Associated Press writers Lisa Leff and Sudhin Thanawala contributed to this report.
Follow Garance Burke on Twitter: (at)garanceburke.