Royal Caribbean said Allure of the Seas was 47 miles east of Fort Lauderdale bound for Nassau Sunday night when a passenger "witnessed another guest going overboard," the Miami Herald reported.
The ship's captain turned around and alerted both the U.S. and Bahamian Coast Guard, the cruise line said in a statement.
A review of closed-circuit camera footage by the ship's crew showed "a 21-year-old female guest from the United States going overboard."
Petty Officer 3rd Class Sabrina Elgammal of the U.S. Coast Guard said Monday's search involved four aircraft crews and a cutter crew, the South Florida Sun-Sentinel reported.
The searchers covered about 320 square miles and intended to keep going "until we've exhausted all our assets," Elgammal said.
The name of the overboard passenger has not been released.