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The latest escalation comes a day after it hit Houthi targets Hodeidah port.
The Houthi's offer of an education for US students sparked a wave of sarcasm by ordinary Yemenis on social media.
Britain and the United States have been launching retaliatory strikes against the Houthis, and the confirmation of fatalities could lead to pressure for stronger military action.
A joint statement said that the militaries of US and UK, with support from Australia, Bahrain, Canada, Denmark, the Netherlands, and New Zealand conducted the strikes.
Houthis have vowed to continue their attacks -- just one part of a growing crisis in the Middle East linked to the Israel-Hamas war.
In a statement on social media platform X, US Central Command said the Houthi missiles presented an imminent threat to merchant vessels and US Navy ships in the region.
The vessel, M/V Gibraltar Eagle, was attacked with an anti-ship ballistic missile.
The Houthis have carried out a growing number of attacks on the key international sea route since the Gaza war erupted with Hamas's unprecedented attack on Israel on October 7.
The Houthis have vowed to attack ships linked to Israel or bound for Israeli ports to show support for Hamas Islamists battling the Israeli offensive in Gaza.
The Huthis have repeatedly targeted vessels in the vital Red Sea shipping lane with strikes they say are in support of Palestinians in Gaza, where Israel is battling militant group Hamas.