The decision, taken on Friday, halts the use of the key transit route until further notice in order to "not take any risks" with its crews and vessels, said the source.
The Huthi rebels, part of the anti-Western, anti-Israel "axis of resistance" of Iranian-backed groups, have been harassing Red Sea shipping for months, triggering US and British reprisal attacks.
The Huthis say they are targeting Israel and Israeli-linked vessels to push for a stop to the offensive in the Gaza Strip, where Israel is battling Hamas militants.
The attacks prompted many shipping companies, including CMA CGM, to avoid the Red Sea, a vital route that normally carries about 12 percent of global maritime trade, for a period in December.
But the detour around southern Africa to avoid the Red Sea, which adds considerable cost and time, led many shippers to resume using the route, although many halted once again in January following a new spate of attacks.
American forces shot down a drone off Yemen on Thursday and later destroyed an explosives-laden uncrewed surface vessel that threatened ships in the Red Sea, the US military said.
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