Earlier on Sunday, the Houthis complained that US aircraft were observed flying close to Yemeni airspace and coastal areas. The group is yet to comment on the incident involving the USS Laboon, a destroyer.
The downing of the missile came after American and British forces began returning fire against the Houthis on Friday in response to the movement’s attacks on shipping in the Red Sea.
The Islamists had warned their response to the strikes in Yemen will be “strong and effective”.
Houthi attacks in the region have snarled commercial shipping through the key waterway, which accounts for about 15 per cent of global sea trade.
The Red Sea crisis has added to anxieties over a wider conflict in the Middle East beyond Gaza, where Israel is waging a campaign to annihilate the Palestinian terror group Hamas, which rules the strip and, like the Houthis, is backed by Tehran.
The Houthis, which gained control over most of Yemen after years of civil war, have framed their attacks in the area as an act of solidarity with the people of Gaza targeted at Israeli-linked vessels.
However, some of the ships they have attacked have no clear connection to Israel.
It is unclear what impact the British and US strikes have had on the group’s capabilities.
Led by the secretive Abdul Malik al-Houthi, the Houthis have amassed significant firepower in less than a decade,
Some experts believe they are now a formidable fighting force, backed by weapons and training supplied by Iran.
The attacks in the Red Sea have led shipping companies to divert vessels away from the area, forcing them to take a longer route around southern Africa instead.
Since Nov 19, the Houthis have carried out at least 27 strikes on cargo ships in the region.
