Tuesday's incident comes as the US military announced it had seized Iranian-supplied weapons bound for the Houthis during an operation last week. Meanwhile, the US has hit more targets in Houthi-controlled areas of Yemen.
An official told CBS, the BBC's American partner, that the US conducted further strikes on Houthi positions overnight.
The US and UK launched a wave of airstrikes against dozens of Houthi targets on Januart 11 following attacks on shipping in the Red Sea.
The Houthis have vowed to retaliate and on Sunday the US said it had shot down a missile fired towards one of its warships from a Houthi area of Yemen.
Several vessels have been targeted by the movement's fighters since November in protest at Israel's war with Hamas.
The Houthis say they are targeting vessels which are Israeli-owned, flagged or operated, or are heading to Israeli ports.
The Red Sea connects the Indian Ocean to the Mediterranean via the Suez Canal but several shipping lines have announced they are now diverting round the Cape of Good Hope to reach Europe instead.
The US said on Tuesday that analysis from the weapons it seized from a ship near the Yemen coast suggested the Houthis had been using the same kind of weapons in their Red Sea attacks.
"This
is the first seizure of lethal, Iranian-supplied advanced conventional weapons
(ACW) to the Houthis since the beginning of Houthi attacks against merchant
ships in November 2023," US Central Command said in a statement.
