The company allegedly works with Selecmark, the Cuban authority which "lends" Cuban workers all over the world.
Human rights organisations and MEPs have claimed that European companies are using Cuban workers in conditions of semi-slavery.
On Wednesday, the NGO Prisoners Defenders, with the support of Human Rights Watch, accused, among others, MSC Cruises, of taking advantage of the situation of workers from the Caribbean island.
The holiday cruise giant is said to be working with Selecmar, the Cuban authority which "lends" Cuban workers all over the world.
According to Javier Larrondo, director of Prisoners Defenders, they have evidence that has been presented to the International Criminal Court.
“We have a lot of proof. These documents detail the terrible conditions of Cuban workers abroad," Larrondo said.
"For example, the confiscation of their property, including documents, and a ban on returning to Cuba for eight years, keeping these workers away from their little children, if they abandon their jobs or fail to return to Cuba at the end of their contracts.
"But we also have Cuban legislation [which confirms that]," he added.
"We also have work certificates from Selecmar that sells Cuban workers for luxury cruises and withholds 80% of the workers' wages and [we also have] certificates from the Cuban Ministry of the Interior proving these allegations. All this is ratified by more than 1111 complaints.”
In a response to Euronews, MSC Cruises said: “Like all shipping companies we had to engage our Cuban crew members through Selecmar since it was a requirement of the Cuban authorities. We have and always will treat all our crew members equally and fairly in terms of salary and working conditions on our vessels regardless of nationality."
The sale of services by Cuba's Selecmar, includes medical and health services, but also the provision of sail crews.
Much of the money obtained, however, does not go to the workers, but to the Cuban government.
According to one of the European Parliament’s vice-presidents, Dita Charanzova, this scandal cannot be tolerated in Europe.
“The European Union has a framework agreement with Cuba and it was actually the European Parliament that had a condition during the ratification process of this agreement, which was a strong Human Rights clause," Charanzova told Euronews. "I think it is really now the time to properly implement and enforce this agreement. And I think that these cases demonstrate the urgency for the European Union to have a ban on forced labor.”
The income international Cuban missions generate is the main source of revenue for the Cuban Government abroad since at least 2005.