Officials said the woman, Claudene Christian, 42, had been unresponsive when taken from the water in a dramatic helicopter rescue.
The ship’s captain is still missing, but 14 crew members were rescued.
The ship, which was built for the 1962 film Mutiny on the Bounty, is thought to have sunk.
HMS Bounty was off North Carolina in a stretch of water known as “the Graveyard of the Atlantic”.
It was approximately 160 miles (250 km) west of the eye of storm Sandy, when it began taking on water on Sunday night.
A coastguard official said earlier that the ship seemed to have capsized while the crew were trying to abandon ship and get into life rafts in 18ft (5.4m) seas.
Fourteen crew members were hoisted to safety by helicopter, but two of the crew appeared not to have made it to the rafts, he said.
Claudene Christian was taken to a North Carolina hospital by helicopter, the coastguard said.
HMS Bounty is a three-mast, 180ft replica of the ship made famous by the mutiny of its crew in Tahiti in 1789.
It had featured in a number of Hollywood films including Pirates of the Caribbean: Dead Man’s Chest.
The replica left the north-eastern state of Connecticut last week and was heading to Florida.
“They were staying in constant contact with the National Hurricane Center,” Tracie Simonin, the director of the HMS Bounty Organization, told the Associated Press news agency.
“They were trying to make it around the storm.”
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