The navy said it had received a distress call on Tuesday when the 14,000-container carrier was about 120 nautical miles (222 kilometres) away from Sri Lanka.
It dispatched a specialist fire-fighting ship to lead a fleet of smaller vessels out to sea to douse the fire aboard the Panama-registered MSC Daniela.
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"There are no casualties among the 22-member crew," spokesman Chaminda Walakuluge told AFP.
"An Indian coastguard vessel which was on a port call to Colombo has also joined the fire fighting effort."
Walakuluge said the cause of the fire was not known.
The vessel has now been guided to a location just north of the Colombo port.
1732354127-0/Untitled-design-(3)1732354127-0-270x192.webp "north america s oldest macaroni penguins mark their 40th year")
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