Last night, the 200 passengers on the Paul Gauguin were asked to stay in their cabins and the ship bound for Rangiroa returned to Tahiti.
Local media said all on board would need to be tested.
There has been no official statement about the situation.
Cruises resumed two weeks ago.
In mid-July, French Polynesia became the first destination in the South Pacific to accept travellers without imposing any quarantine.
All arriving airline passengers have to prove that they are Covid-19 free three days before departure and self-test for the coronavirus four days after landing in Tahiti.