The ship "reported a sound of an explosion in the vicinity of the vessel" southwest of the Yemeni port of Salif, the United Kingdom Maritime Trade Operations said, noting that US-led coalition forces were investigating.
Security firm Ambrey said it was "aware of a 'missile'-related incident west of" the port city of Hodeidah, but did not elaborate.
There was no immediate claim of responsibility for any attack.
But Yemen's Iran-backed Huthi rebels, who control the capital Sanaa and much of the country's Red Sea coast, have launched a flurry of attacks against ships since November, a campaign they say is in solidarity with Palestinians amid the Gaza war.
The attacks have sent insurance costs spiralling for vessels plying the key trade route and prompted many shipping firms to take the far longer passage around the southern tip of Africa instead.
Since January, the United States and Britain have also launched repeated strikes on Huthi targets in Yemen in response to the ship attacks.
The strikes have not thwarted the rebels, who have continued to attack merchant vessels, having since declared American and British ships legitimate targets.
