It wasn't immediately clear what had happened to the oil tanker Sounion, which had been abandoned by its crew on Thursday and reportedly anchored in place.
The Houthis didn't immediately acknowledge the fire. The rebels are suspected to have gone back and attacked at least one other vessel that later sank as part of their months-long campaign against shipping in the Red Sea over the ongoing Israel-Hamas war in the Gaza Strip.
The attacks have disrupted a trade route that typically sees $US1 trillion in goods pass through it annually.
The British military's United Kingdom Maritime Trade Operations centre reported the fires in a note to mariners on Friday night.
"UKMTO have received a report that three fires have been observed on vessel," the centre said. "The vessel appears to be drifting."
A United States defence official, speaking on condition of anonymity to discuss intelligence matters, said American officials were aware of the fires and continued to monitor the situation.
The vessel had been staffed by a crew of 25 Filipinos and Russians, as well as four private security personnel, who were taken by a French destroyer to nearby Djibouti, the European Union's Aspides naval mission in the Red Sea said on Thursday.
The Sounion has 136,000 tonnes of crude oil aboard and represents a "navigational and environmental hazard", the mission warned. "It is essential that everyone in the area exercises caution and refrains from any actions that could lead to a deterioration of the current situation."
Late on Friday night, the Houthis released footage of an explosion striking the Sounion, their fighters on the water in the distance chanting the group's slogan: "God is the greatest; death to America; death to Israel; curse the Jews; victory to Islam."
A frame-by-frame analysis of the video conducted by The Associated Press suggested three simultaneous explosions struck the deck of the Sounion. That signature suggests an attack conducted by planted explosives, rather than a strike by missile or drone.
The Houthis have targeted more than 80 vessels with missiles and drones since the war in Gaza started in October. They seized one vessel and sank two in the campaign that also killed four sailors.
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