According to Celebrity Cruises, the individuals are asymptomatic, in isolation and being monitored by the ship's medical team.
'We are conducting contact tracing, expediting testing for all close contacts and closely monitoring the situation,' the line said.
About 600 passengers on board
About 600 passengers are aboard the 2,100-passenger ship, which is at 30% capacity.
Celebrity Millennium was in Curaçao today after visiting Aruba on Wednesday. Friday is a sea day before arrival back to St. Maarten on Saturday.
The two people are scheduled to disembark there to isolate at a designated facility until they test negative.
Closely watched Caribbean start
Celebrity Millennium departed with fanfare from St. Maarten last Saturday. Apart from SeaDream Yacht Club's short-lived attempt to restart from Barbados last November, no other Caribbean cruises have embarked since the global shutdown so this voyage is being closely watched.
Fully vaccinated voyage
Celebrity Millennium is sailing with fully vaccinated crew and passengers and following comprehensive protocols that, according to a Celebrity statement, 'align with our destination partners and exceed CDC guidelines to protect the health and safety of our guests.
'All guests on Celebrity Millennium were required to show proof of vaccination as well as a negative COVID-19 test within 72 hours before sailing from St. Maarten this past Saturday,' the statement said. 'This situation demonstrates that our rigorous health and safety protocols work to protect our crew, guests and the communities we visit.'