Maersk and other shipping groups have recently diverted vessels away from the area and the Gulf of Aden, which is one of the world's busiest routes.
It follow attacks by Yemen's Houthis.
The Danish firm has been forced to send containers on a long journey around Africa rather than through the Suez Canal shortcut.
Maersk CEO Vincent Clerc said this week the disruption to global shipping caused by the attacks will probably last at least a few months.
That isn't the only problem facing the firm.
Maersk added that winter storms and the effects of the holiday season have led to terminal closures and navigation stoppages in northern Europe.
Container shipping rates for key global trade routes have soared.
U.S. and UK air strikes on Yemen in response to the Houthi attacks have also raised fears of prolonged disruption to global trade traffic in the Red Sea.
