The Houthis said they shot down the Predator with a surface-to-air missile, part of a renewed series of assaults this week by the rebels after a relative lull in their pressure campaign over the Israel-Hamas war in the Gaza Strip.
The US military acknowledged to the Associated Press on Saturday that "a US Air Force MQ-9 drone crashed in Yemen".
It said an investigation was underway, without elaborating.
The Houthis described the downing as happening on Thursday over their stronghold in the country's Saada province.
Footage released by the Houthis included what they described as the missile launch targeting the drone, with a man off-camera reciting the Houthi's slogan after it was hit: "God is the greatest; death to America; death to Israel; curse the Jews; victory to Islam".
The footage included several close-ups on parts of the drone that included the logo of General Atomics, which manufactures the drone, and serial numbers corresponding with known parts made by the company.
The US military says one of its MQ-9 Reaper drones "crashed in Yemen". (HANDOUT/UNIVERSITY OF NSW)
Since the Houthis seized the country's north and its capital of Sanaa in 2014, the US military has lost at least five drones to the rebels counting Thursday's shootdown - in 2017, 2019, 2023 and this year.
Reapers, which cost about $US30 million ($A46 million) apiece, can fly at altitudes up to 15km and have an endurance of up to 24 hours before needing to land.
The drone shootdown comes as the Houthis launch attacks on shipping in the Red Sea and Gulf of Aden, demanding Israel ends the war in Gaza, which has killed more than 34,000 Palestinians there.
The war began after Hamas-led militants attacked Israel on October 7, killing 1200 people and taking 250 others hostage.
The Houthis have launched more than 50 attacks on shipping, seized one vessel and sank another since November, according to the US Maritime Administration.
Houthi attacks have dropped in recent weeks as the rebels have been targeted by a US-led air strike campaign in Yemen.
Shipping through the Red Sea and Gulf of Aden has declined because of the threat.
US officials have speculated that the rebels may be running out of weapons as a result of the campaign against them and after firing drones and missiles steadily in the last months.
However, the rebels have renewed their attacks in the last week.
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