Norwegian Cruise Line, Oceania Cruise and Regent Seven Seas have suspended all sailings from 13 March until 11 April.
In a statement by parent company Norwegian Cruise Line Holdings, it said the move was aimed at contributing to efforts around the globe to contain the spread of the Covid-19 coronavirus.
It added: “This measure is taken in an abundance of caution and the company has not experienced any confirmed cases of Covid-19 across its 28-ship fleet.”
The company said voyages currently under way would conclude and guests disembarked as soon as possible and assisted with travel arrangements.
All customers on impacted voyages will receive a 125% refund of the fare paid in the form of a future cruise credit, which can be applied toward any future cruise through 31 December 2022.