The vessel, built in 1960 for an MGM movie starring Marlon Brando, was en route to Galveston, Texas, the Houston Chronicle reported. Local officials said it was planned to be a tourist attraction on the waterfront.
Capt. Robert Walbridge, 63, disappeared after the crew abandoned ship early Monday about 90 miles off Cape Hatteras, the U.S. Coast Guard said. The search for him was ongoing, the Chronicle said.
Another crew member, Claudene Christian, 43, was unresponsive when pulled from the water and she was pronounced dead at a hospital.
Fourteen people were rescued.
Walbridge, a longtime captain of reproduction sea-going ships, took the helm of the Bounty in 1995, the ship's website indicated.
Christian, a Southern California resident who grew up in Oklahoma, was said to be a distant relative of Fletcher Christian, the ringleader of the 18th-century mutiny aboard the original HMS Bounty.
The 180-foot replica Bounty left New London, Conn., Thursday after crew members of the USS Mississippi helped crew the vessel at the request of its owner, Bob Hansen, the Richmond (Va.) Times-Dispatch reported.
It was built for the 1962 Brando movie "Mutiny on the Bounty" and was used in two "Pirates of the Caribbean" movies, the Chronicle said.