Italy's Costa Cruises said Monday it was isolating more than 700 guests on board its Victoria ship after one of them tested positive for the novel coronavirus.
The company said the unnamed Argentine was "in stable condition at a hospital facility" in Crete, where the person was taken off the ship on Sunday.
A local TV report in Greece identified the Argentine as a 63-year-old woman.
"As a precaution, and in compliance with the health procedures provided on board, the people who came into contact with the guest have been placed in immediate isolation," the cruise company said in a statement to AFP.
"For further precaution the company is proceeding to isolate all guests in their cabins."
Costa said the Victoria had "726 guests of various nationalities and 776 crew members," and was sailing in the eastern Mediterranean.
The company added that it was in contact with Italian authorities and searching for a "suitable port for the ship to dock".
Italy has closed its ports to foreign cruise ships and suspended the operation of its own services in response to the coronavirus pandemic.
The Italian transport ministry said that national ships already at sea would have to return to port and undergo tests on all crew and passengers.
Costa Cruises said it was looking for a port "while respecting the situation that the most affected Italian regions are facing".
Italy's death toll from the pandemic topped 6,000 on Monday.