The Azamara Quest docked in the port of Sandakan, on the island of Borneo.
Fire broke out on the vessel on Friday, a day after it left Manila for Malaysia, carrying 1,001 people, mainly European and American tourists.
Operator Azamara Club Cruises said five crew suffered smoke inhalation, but that no passengers were injured.
After crossing from Philippines into Malaysian waters earlier on Sunday, the liner, travelling at a speed of six knots, was escorted to Sandakan by a Malaysian patrol boat.
Police and buses were waiting at the port to take passengers to various hotels, the Associated Press news agency reports.
The company has said that the rest of the ship’s voyage will now be cancelled and the passengers flown home. The company has also said it will give them a refund.
Earlier this year, 32 people died when a cruise ship owned by another firm – Carnival – ran aground off the coast of Italy.