The decision to stop traffic through the Strait of Hormuz and the Red Sea comes the day after the US and Israel attacked Iran, which then responded with attacks on targets in several countries.
"The safety of our crews, vessels and customers continues to be our top priority," the Danish company wrote in a statement, adding that the announcement is valid until further notice.
Maersk, which only recently resumed traffic via the Suez Canal, is now forced to route its deliveries the long way around the Cape of Good Hope.
Since the violence began on Saturday, there have been several reports that Iran has effectively closed the Strait of Hormuz, the world's most important transport route for oil exports from Gulf countries.
