The accident happened just about 30 minutes after the ship left Jumunjin port on the east coast, Yonhap News Agency reported.
The identity of the victim and the name of the cruise ship have not been disclosed.
Two crew members jumped into the sea to rescue the victim, who was then taken to a nearby hospital for emergency treatment but died later, The Korea Times reported.
The cause of the accident has not been revealed.
Last year a teenage passenger died after falling off a Royal Caribbean cruise ship as it was sailing from Florida to the Bahamas, Business Insider reported.