The cruise ship company MSC has made the procedures, for crew as well as passengers, part of its new health and safety protocols.
The MSC Grandiosa, which was christened last year, set sail from the northern Italian port of Genoa on Sunday evening for a seven-night cruise in the western Mediterranean.
Any one testing positive, or with a fever, or having other Covid-19 symptoms was denied boarding, the company said.
Guest must wear face masks in lifts and other areas where social distancing is not possible.
The crew spent time in quarantine before the start of the cruise.
Earlier this month, the Italian government gave its approval for cruise ships to once again depart from Italy’s ports but limited cruise ships to sailing with 70% capacity.
MSC declined to say how many passengers were sailing on this cruise.
Among the port calls for the Grandiosa, MSC’s flagship, are Naples, Palermo, Sicily and Valletta, Malta.
Malta is one of four Mediterranean countries that Italy now requires travellers arriving from to have Covid-19 tests.
For now, MSC was limiting its guests to the residents of Europe’s 26-nation Schengen visa free travel zone.
MSC said every guest and crew member on board will be given a wristband that “facilitates contactless transactions around the ship as well as providing contact and proximity tracing”.
Cruise ships and the business they bring to many Italian cities during port excursions make up an important segment of Italy’s vital tourism industry.
An estimated 12 million cruise ship passengers arrived or departed from Italian ports last year or made port calls in Italy, according to industry figures.