The fire in an engine room late Friday had been contained but it left the Azamara Quest without propulsion in calm waters in the middle of the Sulu Sea, they said.
As a precaution, the captain had initially asked all passengers to prepare to leave the ship, but an evacuation was not necessary in the end, Azamara Club Cruises said on its web site.
"There were no injuries of guests reported and the atmosphere aboard is calm," it added.
The crew later restored power to one of the ship's engines, allowing the vessel to resume air conditioning, running water, plumbing and refrigeration, it added.
Both the liner and the Philippine Coast Guard said the blaze caused smoke-related injuries to five crew members who were treated on board.
"However, one crew member is more seriously injured and requires additional and urgent medical attention that can only be provided in a hospital," the cruise liner statement said.
Philippine Department of Transportation spokesman Nicasio Conti, speaking on DZBB radio in Manila, said there were about 600 mostly American and European passengers on board.
Coast guard Ensign June Greanata told AFP by telephone from Puerto Princesa, the nearest Philippine port, that a Philippine Navy vessel had been sent to help the stricken vessel.
A Philippine Navy doctor on board will assess whether the seriously injured crew member will require an airlift to hospital, she added.
The nationalities of the injured crew members were not disclosed, although the Philippine transportation department said it was aware about 120 of them are Filipinos.
The Malta-flagged liner, described on its website as a 30,277-tonne vessel with 355 crew and a maximum passenger capacity of 694, said that due to the fire it would abort the voyage when it reaches the Malaysian port of Sandakan.
"Engineers onboard Azamara Quest continue to work on restoring propulsion to the ship. Once they have restored the ship's propulsion, Azamara Quest will sail directly to Sandakan," it added.
The coast guard spokeswoman said its operators, Florida-based Royal Caribbean International, also dispatched a salvage vessel to tow the stricken ship should its onboard engineers fail to get it up and running again.
One option would be to tow the ship to the central Philippine port of Cebu for repairs, she added.
The vessel left Hong Kong on Monday for a 17-night voyage.
It left Manila, its first port call, on Wednesday and had also been due to make port calls on Balikpapan, Palapo, Benoa Bali, Semarang and Komodo in Indonesia before sailing to Singapore.
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