The two guests, who shared a stateroom, are asymptomatic and have been placed in isolation, Celebrity said in a statement.
The cases were identified through routine testing ahead of the ship’s departure from St Maarten on Saturday (5 June).
Millennium is sailing a seven-night itinerary, calling in Barbados, Aruba and Curacao. Around 500 passengers are onboard, in excess of 95% of whom are fully vaccinated against Covid-19.
All crew are also required to be fully vaccinated.
"We are conducting contact tracing, expediting testing for all close contacts, and closely monitoring the situation," said Celebrity.
