The Liberian flagged, Greece-owned and operated bulk carrier was hit by a remote-controlled sea drone and an aerial projectile southwest of Hudaida on June 19.
A ship is thought to have sunk in the Red Sea after a deadly attack by Houthis that forced it to be abandoned last week, a security agency has said.
The MV Tutor, which was holed during an attack that left one Filipino sailor dead, is "believed to have sunk", the United Kingdom Maritime Trade Operations said late on Tuesday.
"Military authorities report maritime debris and oil sighted in the last reported location," said UKMTO, which is run by the British Navy.
The Liberian flagged, Greek-owned and operated bulk carrier was hit by a remote-controlled sea drone and an aerial projectile southwest of Hudaida on June 19.
It was evacuated in a military operation on Friday and left drifting, its engine room breached and taking on water.
Second sunken ship
The Houthis have launched scores of drone and missile attacks on the vital sea route since November, in retaliation for Israel's war on Gaza.
The Tutor appears to be the second ship sunk by the Houthis in recent months after the Rubymar, carrying thousands of tonnes of fertiliser, went down in the Red Sea in March after a missile strike.
In addition, US National Security Council spokesman John Kirby said a Sri Lankan crew member was critically wounded in a separate Houthi attack on the MV Verbena on Thursday.
The Houthis, who seized Yemen's capital Sanaa in 2014, have been at war with a Saudi-led coalition since 2015.
The UN says the conflict has left hundreds of thousands of people dead, through fighting or indirect causes like lack of food, and created one of the world's worst humanitarian crises.