The tanker "Overseas Raymar" struck the bridge about 11:20 a.m. while headed out to sea, the Coast Guard said.
Coast Guard investigators were headed to the scene, spokeswoman Lt. Heather Lampert said.
She said the ship was from the Marshall Islands, but she did not immediately have additional details.
California Department of Transportation spokesman Bart Ney said a tower of the west span of the bridge was struck, and the ship appears to have moved on. Maintenance crews were heading out to inspect the structure, he said, although the tower appeared fine from a distance.
Ney said there is a fender system that has been built onto the west span that normally can absorb such strikes.
The strike came more than five years after the container ship Cosco Busan slammed into the bridge on a foggy morning and dumped 53,000 gallons of oil onto the water.
No one was injured but the spill contaminated 26 miles of shoreline. It also killed more than 2,500 birds of about 50 species and delayed the start of the crab-fishing season.
The cleanup cost exceeded $70 million. The 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.