"Explosions heard, missiles were sighted" near the port of Hodeida on Yemen's west coast, UKMTO said, adding that the ship and its crew are safe.
It followed two other explosions earlier Tuesday that struck near a vessel also off Hodeida, according to the British maritime authority.
The ship later continued its voyage, without reporting any major damage or crew injuries, UKMTO said.
There was no immediate claim for Tuesday's attacks.
But Yemen's Iran-backed Huthi rebels have launched a flurry of drone and missile strikes targeting commercial vessels transiting the Red Sea in recent weeks.
They say their strikes are in solidarity with Gaza, where Israel striking and bombing the Palestinian territory.
According to the Pentagon, the Huthis have launched more than 100 drone and missile attacks, targeting 10 merchant vessels involving more than 35 different countries.
The attacks are endangering a transit route that carries up to 12 percent of global trade, prompting the United States to set up a multinational naval task force to protect Red Sea shipping.
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