The unnamed Italian family had disembarked at the port of Naples on an organised day trip to the nearby island of Capri – but then left the group and ventured forth on their own despite being told not to, MSC said.
The family was later refused entry back on the ship, and they were left behind at Naples.
“By departing from the organised shore excursion, this family broke from the safe 'social bubble' that MSC Cruises created for them to safely enjoy their visit ashore, and therefore could not be permitted to re-board the ship,” it said in a statement.
Staff scan pasengers' temperatures ahead of boarding the MSC Grandiosa cruise ship. Photo: AFP
The MSC Grandiosa, part of the fleet of privately owned MSC Cruises, was the first major cruise line to take to the Mediterranean after Italy’s long coronavirus lockdown.
It departed from Genoa on Sunday for a seven-day tour, after being out of action for more than six months.
Its cruises are to sail at 70 percent passenger capacity, as part of a series of measures taken to reduce the risk of coronavirus infection on board, though company representatives said this particular voyage was at closer to 50 percent capacity.
MSC is taking a tough line as it tries to avoid the problems experienced by smaller cruise operator, Norway's Hurtigruten, earlier this month, when dozens of passengers and crew tested positive for COVID-19.
Health authorities fear passengers may have infected locals at ports up and down the Norwegian coast during day trips.
MSC said its security protocol exceeds national and industry standards. It says it pre-screens sites to be visited to make sure social distancing can be maintained, sterilises vans and buses before trips, and ensures that tour guides and drivers are properly equipped with masks.
The global cruise industry, which is slowly trying to get back on its feet after travel stopped during lockdown, has been criticised by health authorities for mishandling the epidemic in its early stages.