The United Kingdom Maritime Trade Operations reported two missiles in the vicinity of the vessel.
"The first was intercepted" by US-led coalition forces, it said.
"The second impacted the water a distance from the vessel," it added, noting that "the vessel reports no damage and the crew are reported safe".
Maritime security firm Ambrey also said "a vessel was targeted... southwest of Hodeidah," but did not provide additional details.
There was no immediate claim of responsibility for the reported attack, which coincides with a campaign by Yemen's Iran-backed Huthi rebels against ships linked to Israel, Britain or the United States.
The rebels have launched dozens of missile and drone strikes on shipping in the Red Sea and the Gulf of Aden since November, actions they say are in solidarity with Palestinians during the Gaza war.
The United States, which leads an multi-national flotilla intended to protect Red Sea shipping, has since mid-January launched repeated trikes on Huthi targets in Yemen. Britain has also participated in several of the strikes.
In a televised speech on Thursday, Huthi chief Abdul Malik al-Huthi said 37 people had been killed in more than 400 strikes by the US and Britain on Yemen since January.
"During these operations and attacks, 37 martyrs died and 30 others were wounded," he said, without specifying if the casualties were civilians or combatants.
The rebel leader vowed to continue the attacks on Red Sea shipping, saying his fighters launched 34 attacks in the past month.
Most of the attacks have been by drone or missile, but in November the Huthis seized the vehicle-transporter Galaxy Leader and its crew.
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