The pair were traveling on the MSC Seaside cruise ship and disembarked with their families in Syracuse, Sicily, on Tuesday, MSC told CNN on Wednesday. The two passengers were asymptomatic.
The cruise had previously docked in Malta but the passengers were forbidden to disembark as the ship only made a "technical" call, according to the cruise operator, which would not disclose the nationality nor the total number of passengers on board.
All passengers traveling with MSC must have a Covid-19 test 96 hours before departure, another when they embark, and a third during the cruise. MSC does not require passengers to be vaccinated, but the rules apply to those who have been.
Guests on board are required to wear masks in public spaces and social distance.
"Our protocol is working, if not on board those two people would still be freely circulating," said MSC spokesperson Michele Curatolo.
The company has a contigency plan for each port of call, added Cuartolo, which meant that a "protective transfer was immediately activated" for the two passengers who tested positive.
Luca Biondolillo, chief communications officer of MSC Cruise, said that three of the company's vessels are currently at sea, a number due increase to eight by August.
In August 2020, MSC cruises was the first major cruise line to resume sailing in Europe after the first wave of the Covid-19 pandemic subsided.
The cruise line has been running Italian sailings on and off since then, and recently launched the UK's first cruise in over a year.
Those wishing to take a cruise from the United States have had to put their plans on hold due to the pandemic, but there's hope on the horizon.
Sailings on numerous cruise lines are slated to embark from US ports within the next month, nearly 15 months after a no-sail order from the US Centers for Disease and Control and Prevention brought cruises to a halt.
Most ships are still awaiting CDC approval to sail. Since October of last year, the agency has issued a series of evolving requirements and guidelines in the form of a Conditional Sailing Order.
Francesca Street contributed to this story