He said there were no reports that any of the 708 crew and passengers, who were mostly Dutch, had sustained injuries and the 11,162-tonne Calypso was making good progress in calm seas.
Rescue services were scrambled in the early hours after a distress call was received at about 0300 GMT from the ship.
Lifeboats and a coastguard helicopter were sent to the stricken liner, but crew members had put out the fire in the engine room before they arrived.
"They smothered the engine room with CO2, which is normal procedure, and they have managed to extinguish the fire," said an official in the port of Dover, where the coastguard is co-ordinating the rescue.
"There are no injuries to passengers or crew. The majority of the passengers are Dutch."
The liner is being towed to port by a tug because its engine cannot be restarted.
The Calypso was heading from the English port of Tilbury to St Peter Port in Guernsey in the Channel.
According to travel websites, the ship was built in 1968, has 243 cabins and can carry up to 593 passengers.