The two guests were sharing a room onboard the Celebrity Millennium, which is part of Celebrity Cruises owned by the Royal Caribbean Group.
It was the first ship with paying customers to sail from North America since the start of the coronavirus pandemic, reports said.
The two passengers are asymptomatic but in isolation while the cruise line conducts contact tracing, the statement said.
All passengers and crew have to show proof that they're fully vaccinated, reports said.
"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."