All crew and adult passengers on board the Celebrity Millennium had to show proof that they were fully vaccinated as well as provide a negative COVID-19 test prior to or at the time of boarding.
The passengers found out they were positive while undergoing testing before disembarking the ship in St. Maarten. All of their close contacts tested negative, according to Celebrity.
"The individuals are asymptomatic and currently in isolation and being monitored by our medical team," the cruise line said in a statement to ABC News. "We are conducting contact tracing, expediting testing for all close contacts and closely monitoring the situation."
A spokesperson for Celebrity explained the two positive passengers will remain in St. Maarten until they test negative, and then the cruise line will help them make travel arrangements to go home.
The Millennium is the largest COVID-19-vaccinated cruise in the world so far.
Celebrity referred to vaccines as "game changers" in allowing them to restart operations.
The ship, which usually holds more than 2,000 people, is operating at about 30% capacity.
"There will be no masks or social distancing required because our occupancy is low," Celebrity CEO and President Lisa Lutoff-Perlo explained to ABC News before the cruise began. "The guests are going to have plenty of space, with plenty of dining options and activities."
Celebrity made some adjustments to their operations -- they traded their usually crowded muster drill with an online version, and self-serve buffets are no longer an option. Their infirmary is now staffed with two doctors and 11 nurses, and they've added more ventilators on board and isolation rooms.
The Centers for Disease Control and Prevention still recommend against cruise travel, but it recently gave Celebrity the green light to sail the first cruise out of the U.S. at the end of the month from Ft. Lauderdale, Florida.