MOSCOW (Sputnik) — According to the CNBC television channel, the 704-passenger vessel left Miami at 16:00 [20:00 GMT] on Sunday. The cruise is expected to reach Cuba at 10:00 local time [14:00 GMT].
The cruise ship, called Adonia, is part of the "impact travel" program which envisages travellers not only taking part in leisurely activities but also working with locals at each stop.
US tourists are currently not allowed in Cuba, but may qualify for one of 12 categories, including "people-to-people" and "cultural exchange" programs which Carnival, the company running the cruise, offers.
Relations between Washington and Havana started to improve after President Barack Obama announced in December 2014 a historic shift in US policy, including the loosening of a decades-old trade and travel embargo on Havana.
The two countries reopened embassies in their respective capitals in the summer of 2015, after more than 50 years of diplomatic non-engagement.
In April, Carnival announced that it would offer the 7-day trips every other week.