The decision comes after a spate of attacks on vessels launched from a part of Yemen controlled by the Houthis - an Iran-backed rebel movement.
The group has declared their support for Hamas and say they are targeting ships travelling to Israel. The Red Sea is one the world's most important routes for oil and fuel shipments.
"The recent attacks on commercial vessels in the area are alarming and pose a significant threat to the safety and security of seafarers," Maersk said in a statement sent to the BBC.
"Following the near-miss incident involving Maersk Gibraltar yesterday and yet another attack on a container vessel today, we have instructed all Maersk vessels in the area bound to pass through the Bab al-Mandab Strait to pause their journey until further notice," it added.
Maersk pausing its Red Sea shipping journeys "could not come at a more difficult time", director general at the Institute of Export & International Trade Marco...
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