23 crew members were evacuated after the ship caught fire in the Arabian Sea, but four are still missing.
The ship, the Maersk Honam, was still on fire on Wednesday morning with the situation regarded as critical.
"We have received news of the Maersk Honam and four missing crew members with deep regret, and will do all we can in the ongoing rescue operation," said Søren Toft, director of operations with Maersk Line.
The ship is reported to have been en route from Singapore to Suez in Egypt and is currently 900 nautical miles southeast of the Omani coastal city of Salalah.
Initial attempts by the crew to put out the fire are reported to have failed.
Several other of the company's ships have been diverted from nearby waters to assist in rescue operations, including the MSC Lauren, Edith Maersk and Gerd Maersk.
The Maersk Honam, a 353-metre long, 53.5-metre wide container ship built in 2017, is currently carrying 7,860 containers. Its capacity is 15,000 containers.
Its crew is made up of nationals of India, the Phillippines, Thailand, Romania, South Africa and the United Kingdom.
The cause of the fire is currently unknown, according to Maersk Line. The company is working to contact relatives of the crew.
"The evacuated crew has naturally been affected," Toft said.
Two of the rescued crew members are reported to have received medical attention.