Costa Allegra, which started drifting in the Indian Ocean after an engine room fire, is being towed by an ocean-going fishing boat to a nearby island.
The vessel, with more than 1,000 people on board including 31 British passengers, is owned by the same company as the Costa Concordia, on which at least 25 people died when it ran aground off Italy last month.
Seychelles Tourism Authority chief executive Alain St Ange said: “It is now being towed to Desroches Island where there is a luxury resort and passengers can at least take a shower before they are flown to Mahe.”
Desroches Island is about 144 miles southwest of Mahe, the main island in the Seychelles archipelago.
But there may not be enough accommodation or flights out of the Seychelles, an archipelago with a population of just over 80,000.
“We are in talks with the ship's agent regarding what to do next but we are making plans to fly them here, although we do not have enough hotel accommodation for all the passengers since we already have heavy bookings because of an international carnival due to start on Friday,” said St Ange.
He added that the next move would be to fly Costa Allegra's 636 passengers and 413 crew out of the country, but he feared there may not be enough seats on the four flights scheduled to leave the country on Tuesday.
The tourism board head said arrangements would be made to tow the ship to Mahe “but it will take a day or two to reach here”.
The blaze broke out in the electrical generators room of the 20-year-old vessel yesterday and was swiftly extinguished with no injuries.
Costa Cruises said: “Currently, Costa Allegra is steady and conditions are safe. Costa Cruises is keeping in touch with guests' families via their emergency contact numbers.
“The line is also communicating with the families of crew, most of whom are Italian and eastern European, through local crew-recruiting organisations.
“Costa Allegra is in compliance with all certificates required by both national and international regulations. Moreover, in October 2011 the ship received its regularly scheduled maintenance in dry dock.”
Two tug boats from the Seychelles are expected to reach the vessel later and will it tow it back under military escort. Somali pirates are active in the region but have not been sighted near the ship.
Costa was reported as saying the ship is not expected to reach land until tomorrow.