The Rubymar cargo ship, attacked last month, has sunk in the southern Red Sea, Yemen's internationally recognised government said in a statement on Saturday.
If verified, it would be the first vessel lost since the Houthis began targeting commercial shipping in November.
The government statement said the ship sunk on Friday night and warned of an "environmental catastrophe".
The ship was carrying more than 41,000 tons of fertiliser when it came under attack, the US military's Central Command previously said.
The Houthis have been attacking commercial ships in the Red Sea region since mid-November, saying they are acting in solidarity with Palestinians in Gaza.
On Monday, a Yemeni government team visited the Rubymar, a Belize-flagged, UK-owned cargo ship, and said it was partially submerged and could sink within a couple of days.
The US military previously said the attack had significantly damaged the freighter and caused an 29 km. oil slick.
The United States Navy's Fifth Fleet did not immediately respond to a request to confirm the sinking on Saturday.
In two separate reports on Saturday the United Kingdom Maritime Trade Operations (UKMTO) agency said it had received a report of a ship being attacked 15 nautical miles west of Yemen's port of Mokha.
"The crew took the vessel to anchor and were evacuated by military authorities," the UKMTO said in an advisory note.
Separately, the UKMTO reported a ship sinking.
Neither report named the Rubymar though both incidents occurred in the vicinity of where the Rubymar was last seen.
Houthi attacks have prompted shipping firms to divert vessels on to the longer, more expensive route around southern Africa. They have also stoked fears that the Israel-Hamas war could spread, destabilising the wider Middle East.
The United States and Britain began striking Houthi targets in Yemen in January in retaliation for the attacks on shipping in the Red Sea, Bab al-Mandab Strait and Gulf of Aden.