The incident happened on the 6,680-passenger vessel as it journeyed between Barcelona and Valencia during the first night of its repositioning sailing to Fort Lauderdale on Sunday (29 October).
According to Cruise Hive, passengers onboard the ship heard an emergency call just after 11pm. The ship immediately diverted from its course for around an hour while the water was searched, it is reported.
Soon afterwards, the ship’s captain announced the rescue had been successful and the individual was receiving care in the ship’s medical centre. An investigation is under way.
The ship has resumed its itinerary and is due to arrive in the US on 12 November as scheduled.
Royal confirmed the guest was "successfully recovered" and brought on board, adding: "Our care team is now offering assistance and support to them and their travelling party.
"Out of privacy for the guest and their family, we have no additional details to share."