"While en route, both ships reported seeing explosions close by and the U.S. Navy accompaniment also intercepted multiple projectiles," Maersk said in a statement, adding it was suspending Red Sea transits by vessels of the U.S. subsidiary.
Both vessels are operated by Maersk Line, Limited (MLL), its U.S. subsidiary that carries cargo for the Department of Defense, Department of State, USAID, and other U.S. government agencies.
They are both enrolled in the Maritime Security Program (MSP) and Voluntary Intermodal Sealift Agreement (VISA) with the U.S. government, which is why they were escorted through the strait by U.S. Navy vessels, Maersk said.
MSP and VISA are programmes run by the U.S. Defense Department to transport forces, supplies and equipment during times of war or national emergency.
The vessels and crew were unharmed and were being escorted back to the Gulf of Aden by the U.S. Navy, Maersk said. Bab al-Mandab is the outlet of the Red Sea, between Yemen on the Arabian Peninsula, and Djibouti and Eritrea on the African coast.
Yemen's Houthi forces on Wednesday fired three anti-ship ballistic missiles toward the U.S.-flagged container ship Maersk Detroit as it was transiting the Gulf of Aden, the U.S. Central Command said separately.
There were no reports of injuries or damage to the ship, it added in a statement.
"Following the escalation of risk, MLL is suspending transits in the region until further notice," it said on Wednesday.
Seafarers remain in the firing line, and have signed agreements to receive double pay when going into the high risk zones.
"There's a feeling of vulnerability," Stephen Cotton, General Secretary of the International Transport Workers' Federation, the leading union for seafarers, told Reuters.
"The feedback from the (ship) captains is certainly on the container trades, they are much happier to go around the Cape."
U.S. maritime labour organizations have been separately concerned about the impact on U.S. flagged ships, which in recent weeks have been subjected to what nine unions called "the most significant attacks on the United States Merchant Marine in more than half a century".
"It is critically important that U.S.-flag vessels carrying commercial, military and foreign aid cargoes are provided the necessary protection from the United States military as they transit the increasingly treacherous waters of the Red Sea," the unions wrote in a Jan. 19 letter to the U.S. Transport Command.
