The yacht and its crew were detained when the boat docked in Crete, the largest of the five Greek islands, to refuel, CNN reported Thursday.
Greek officials didn't say what they intend to do with the yacht or its passengers.
"Authorities are following the necessary legal procedures," including "checking the identities of the passengers" and "the ship's documents," said Elias Sambatakakis, a spokesman for the Greek Coast Guard.
Sambatakakis said the boat's captain and crew have been cooperative.
"It is not yet clear what will happen once procedures are completed," Sambatakakis said. "Obviously if the ship asks for permission to go to Gaza, this will be declined."
The French vessel was the last boat in a flotilla of 10 ships attempting to get to Gaza. Israeli authorities have said the boats are used to smuggle weapons.
Gaza is run by Hamas, a group that has carried out dozens of terrorist attacks. The United States lists it as a terrorist organization.