The woman was Rina Patel, 32, of Interlaken, New York, the Coast Guard said in a statement.
While witnesses said they saw her fall off the 11th deck of the Carnival Ecstasy at 2:30 a.m., the cruise ship company released a statement saying she was "witnessed jumping overboard."
She was wearing a white dress with a pink floral pattern, the Coast Guard said.
The ship was 27 miles southwest of Freeport, Bahamas, when Patel went overboard. That's due east of Fort Lauderdale, Florida, but at least dozens of miles from the US coastline.
The Carnival crew notified the 7th Coast Guard District Command Center, which launched a search operation.
Shannon Parks of Ocean Isle Beach, North Carolina, said she was sleeping when the crew sounded a ship-wide alert.
"It was one of those surreal things where it came on and they said it and you had to stop and think, 'Did they just say man overboard?' And then they repeated it four more times," she told CNN.
The search operation was coordinated with Air Station Miami MH-65 Dolphin helicopter crews, Air Station Miami HC-144 Ocean Sentry airplane crews, and two Coast Guard cutters.
On social media, Parks shared images of a search plane flying over the cruise ship at dawn. In another photo, taken around 3:40 a.m. ET, a small search vessel cuts through the dark water, its path illuminated by a flare.
Though the search effort spanned more than 2,800 square miles, it was not successful in locating Patel, according to the news release.
"We would like to extend our deepest condolences to the loved ones and all that have been affected by this tragedy," said Capt. Todd Coggeshall, chief of response management for the 7th District.
According to Carnival, the 855-foot Ecstasy carries up to nearly 3,000 passengers and crew.
Billed as family-friendly and affordable, the ship departs from Charleston on four- and five-day cruises with stops in Bahamian ports of call, including Nassau, Freeport and Half Moon Cay.