The USS Mason "detected two inbound missiles" within an hour of each other from around 7:00 pm (1600 GMT) on Sunday, said US Naval Forces Central Command spokeswoman Paula Dunn.
The destroyer had been "conducting routine operations in international waters" at the time, she said in a statement.
"Both missiles impacted the water before reaching the ship," said Dunn, adding that "there were no injuries to our sailors and no damage to the ship".
The Huthis described as "unfounded" reports they fired missiles at the US destroyer.
Also Read
Rebel forces "did not target any warships," said a spokesman quoted by the insurgents' sabanews.Net website.
Also on Monday, the Arab coalition fighting the Huthis accused the rebels of firing a ballistic missile towards the southwestern Saudi city of Taif.
The missile was one of two which the Saudi-led coalition intercepted on Sunday, the coalition said, adding the other was launched toward Marib, east of Yemen's rebel-held capital Sanaa.
That attack, which was carried out on October 1, was claimed by the Shiite rebels.
The UAE is a key member of a Saudi-led coalition that has been fighting the Yemeni rebels since March last year.
Coalition warships have imposed a naval blockade on rebel-held ports along Yemen's Red Sea coast allowing in only UN-approved aid shipments.
In its statement on Monday, the US navy said the United States remains "committed to ensuring freedom of navigation everywhere in the world".
The missile fire comes after the Iran-backed rebels blamed the coalition for an air raid that killed more than 140 people and wounded at least 525 on Saturday at a funeral in Sanaa.
Disclaimer: No Business Standard Journalist was involved in creation of this content