Story highlights The missing passenger is a 21-year-old woman from Tennessee

The search area spans about 320 square miles off Florida

A closed-circuit camera recorded the woman going overboard

Coast Guard crews searched Monday for a cruise ship passenger who went overboard Sunday night about 47 miles east of Fort Lauderdale, Florida, officials said Monday.

Another passenger saw the 21-year-old woman from Bartlett, Tennessee, go overboard, according to a statement from the Royal Caribbean International cruise line.

The ship, the Allure of the Seas, left Fort Lauderdale on Sunday for its first port of call: Nassau, Bahamas.

After the woman went overboard, the captain immediately stopped the ship and turned around to search for her, according to Royal Caribbean. Two other nearby cruise ships joined the search, and the Coast Guard later took over.

The site of the woman's disappearance was marked by the ship's GPS, and closed-circuit camera footage shows her going overboard, the cruise line added.

Four Coast Guard aircraft crews and a cutter crew are involved in the search, according a news release from the 7th Coast Guard District. The search area spans about 320 square miles.

"Royal Caribbean's Care Team is providing support to the guest's family, and our thoughts and prayers are with them," the cruise line said.