The 45-foot Neptune hit the shoal around 8:42 p.m. and started taking on water after the impact left a 1-foot gash in the side of the boat, U.S. Coast Guard spokesman Lt. j.g. Josh Dykman said.
The boat's captain tried to steer the stricken vessel to San Francisco's Pier 39. But the boat started having rudder issues and began to sink about 300 feet from the pier, Dykman said.
Three Coast Guard boats took all 22 passengers and crewmembers off the vessel and brought them to the pier, Dykman said. San Francisco fire and San Francisco police boats also responded. There were no injuries.
"We were only in the boat for maybe about 20 minutes or so," Matthew Rice, the party's guest of honor, told KGO-TV. "We were coming around Alcatraz checking it out and all of a sudden it was like boom, just like a big jolt and the next thing we knew the Coast Guard boats came in and got us off."
The Neptune is a 1958 motor vessel operated by San Francisco Bay Boat Cruises LLC, which offers "specialty voyages" on San Francisco Bay, according to the company's website.
The boat is certified to carry 42 passengers, according to the company.
Requests from The Associated Press for comment about the incident weren't immediately returned by officials at the boat cruise company.
The cause of the incident is under investigation. The damaged boat was towed to Sausalito Boat Works where it will be repaired. There were no reports of pollution, Dykman said.