The MSC Daniela sent a distress at 11am on 4 April about 120nm off the coast of Sri Lanka. The vessel later moved within 30 nm of the Sri Lankan coast as vessels were dispatched to tackle the blaze.
According to reports three Sri Lankan naval vessels are helping fight the fire with two Indian coastguard vessels also joining the effort.
No injuries are reported from the 22 crew onboard the MSC Daniela.
MSC said that the fire was brought under control at approximately 0630hrs local time on Wednesday 5 April.
"MSC is currently in discussion with the local authorities to berth the vessel at the appropriate time. Once the ship is considered safe, an investigation into the cause of the fire will be formally initiated," the company said.
"The extent of the damage and cargo losses will not be known until the vessel has safely berthed and has undergone a thorough inspection. Customers with cargo on-board the MSC Daniela should contact their local MSC office."
The Panama-flagged was reported to be sailing from Singapore to Egypt.