The single-engine Cessna 210 Centurion plane hit shallow water around 1:50 p.m. about a quarter-mile north of the San Francisco-Oakland Bay Bridge, prompting the rescue of the pilot and passenger.
Both appeared to be in good condition with no serious injuries, U.S. Coast Guard Lt. Amy Marrs said.
Preliminary reports indicate the plane began to experience engine trouble before it went down, but FAA spokeswoman Ian Gregor said an investigation into the cause by the FAA and National Transportation Safety Board could take months.
Crews began removing the plane around 8 a.m. and will take it to Sacramento, where it will be examined, U.S. Coast Guard Petty Officer Ian Petrie said.
"Crashes are rare but they occasionally happen," FAA spokesman Gregor said. "Cessna is a very popular, common (and) affordable aircraft. There's a lot of them flying around."