President Barack Obama authorized the Tomahawk cruise missile strikes, which were launched at 4:00 am local time (0100 GMT) by the destroyer USS Nitze against Huthi-controlled territory on Yemen's Red Sea coast, a US official said.
"Initial assessments show the sites were destroyed," Pentagon Press Secretary Peter Cook said in a statement.
The strikes "targeted radar sites involved in the recent missile launches threatening USS Mason and other vessels operating in international waters in the Red Sea and the Bab al-Mandeb," it added.
"These limited self-defense strikes were conducted to protect our personnel, our ships, and our freedom of navigation in this important maritime passageway."
The USS Mason, a destroyer, was targeted on Wednesday. The missile fired from rebel-held territory crashed into the ocean before reaching its target.
The Mason and the USS Ponce, an amphibious staging base, were previously targeted on Sunday by two missiles that also fell short.
"The United States will respond to any further threat to our ships and commercial traffic, as appropriate, and will continue to maintain our freedom of navigation in the Red Sea, the Bab al-Mandeb, and elsewhere around the world," Cook said.
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- 'Immediate review' -
The United States is backing a Saudi-led coalition fighting the Iran-backed rebels and the forces of former Yemeni president Ali Abdallah Saleh.
The US military provides intelligence and refueling for Arab coalition aircraft conducting air strikes against the rebels. It also supplies advanced munitions and logistics support to the Saudi-led war effort, and is the kingdom's biggest arms supplier.
But US air forces are not directly involved in strikes in Yemen, which are increasingly criticized by the international community for their devastating impact on civilians.
After Saturday's deadly air strike by the Saudi-led coalition on a funeral in Yemen that killed more than 140 people, the US administration announced an "immediate review" of its cooperation.
The Riyadh-led coalition fighting the Huthis has accused rebels of firing a ballistic missile on Sunday toward a Saudi air base in the southwestern city of Taif, hundreds of kilometers (miles) from the Yemeni border.
The incidents come after the United Arab Emirates, a key member of the Saudi-led coalition, said last week that Yemeni rebels had struck a "civilian" vessel in the strategic Bab al-Mandeb waterway, wounding crewmen.
That attack was claimed by the Shiite rebels.
Coalition warships have imposed a naval blockade on rebel-held ports along Yemen's Red Sea coast allowing in only UN-approved aid shipments.
Supported by Iran, the Huthis swept into the Yemeni capital Sanaa in September 2014 and advanced across much of the country, forcing the government of President Abedrabbo Mansour Hadi to flee.
The conflict has killed more than 6,700 people -- almost two-thirds of them civilians -- and displaced at least three million since the coalition launched military operations, according to the United Nations.