Twelve people were on board. Two people were injured, one of whom died. The second person's injuries were not life-threatening.
The capsized boat, a catamaran, is part of the Swedish Artemis Racing team. It capsized about 1 p.m. near Treasure Island.
The deceased sailor was identified as double gold medalist Andrew Simpson, 36, from the U.K. He was trapped underwater underneath the boat for at least 10 minutes.
The cause of the accident was under investigation. The catamaran was being towed to shore.
People on the boat reportedly jumped from the boat to swim to support boats.
This is the second time a sailor has died during training for the America's Cup. In 1999, Martin Wizner of the Spanish Challenge died almost instantly when he was hit in the head by a broken piece of equipment.
No deaths have been recorded during the actual racing since its inception in 1851.
Simpson and his partner Iain Percy won an Olympic gold medal for England in 2008 in the so-called Star class of sailing. The duo was expected to repeat in London in 2012 but was upset by a Swedish team and settled for silver.
The America's Cup race is scheduled from July through September.
The Associated Press contributed to this report.