Maritime security firm Ambrey said a vessel operating south of Yemen's port of Aden had reported an explosion on board but it did not name the ship.
Meanwhile, the US has launched new air strikes in Yemen, targeting 10 drones reportedly being set up to launch.
According to Reuters, KOI is a Liberian-flagged container ship operated by UK-based Oceonix Services. The same company's fleet includes the oil tanker Marlin Luanda, which was damaged by a missile on Saturday.
The Houthis regard all Israeli, US and British ships as legitimate targets following Israel's war on Hamas in Gaza, and US and British targeting of Houthi missile positions in what the two countries say are efforts to protect commerce.
Houthi military spokesperson Yahya Sarea said on Wednesday that the movement's armed forces had targeted an American merchant ship named KOI with "several appropriate naval missiles".
The ship, he said, had been heading to "the ports of occupied Palestine", a phrase which is sometimes used to mean Israel.
Yemen, he added, would not hesitate to retaliate against British-American escalation.
US Central Command said the 10 drones being prepared for launch in Yemen had posed a threat to merchant vessels and US warships in the region.
All 10 were destroyed along with a Houthi drone ground control station, it said.
The US added that one of its warships had shot down three
Iranian drones and a Houthi anti-ship ballistic missile in the Gulf of Aden.
