The ship, the Charo, which had been at sea for a month, had anchored in an uninhabited bay off Nuku Hiva yesterday where doctors tested all sailors.
One of the crew was flown by the French military from Nuku Hiva in the Marquesas to the main hospital in Tahiti in an operation which also involved the urgent medical aid service, SAMU, and the Joint Rescue Coordination Centre in Tahiti.
A government statement said the patient, who was described as a suspected Covid-19 case, was put on reanimation and kept in isolation to protect other patients.
The government said the ship had been ordered to move back into international waters and to stay near Tahiti.
French Polynesia, which had 60 Covid-19 cases, lifted all restrictions related to the pandemic from today.