The USS Mason was targeted late Wednesday by missiles from territory controlled by the Houthis -- a minority Shia group that has taken control of swathes of Yemen, including the capital, Sanaa.
The strikes marks the first instance of the US firing at Houthi targets since the Yemen civil war erupted in March last year.
The same warship was targeted Sunday, when two missiles were launched within 60 minutes of each other, but in both incidents they missed the ship and landed in the water. The guided-missile destroyer was not damaged in either incident, officials said.
The US warship was conducting routine operations in international waters off the Yemen coast when it was targeted Wednesday, the Pentagon said.
The Houthis have denied carrying out the attacks.
'We will respond to this threat'
The Pentagon said its destroyer USS Nitze launched Tomahawk cruise missiles targeting the coastal radar sites controlled by the Houthi group in "self defense."
Another official said initial assessments indicated all three targets were destroyed, and that the strikes were in remote areas with little risk of civilian casualties or collateral damage.
"USS Mason will continue its operations. Those who threaten our forces should know that US commanders retain the right to defend their ships, and we will respond to this threat at the appropriate time and in the appropriate manner," Pentagon press secretary Peter Cook said in a statement.
"USS Mason will continue its operations."
Houthis: Accusations a 'distraction'
A Houthi military official said "there is no truth to these allegations" in response to Wednesday's incident. Houthi militias had "nothing to do with this act," the Houthi-affiliated SABA news agency reported.
After Sunday's reported missile attack, the military had said that the accusations were aimed at covering up a "heinous" Saudi-led coalition airstrike on a funeral service Saturday in Sanaa that killed at least 155 people.
The US has come under increased pressure over its support of the Saudi-led coalition in Yemen, as the coalition continues to bombard schools and hospitals.
The US had backed the formally recognized government of President Abd Rabbu Mansour Hadi, whose government has been essentially forced from Sanaa to Aden. Hadi himself is believed to be in exile in Saudi Arabia, as are several senior members of his administration.
The Houthis support the former president, Ali Abdullah Saleh.
Calls for world to suspend Saudi arms sales
Last week, the US said it was re-evaluating its support after the deadly funeral airstrike blamed on the Saudi-led coalition. "The United States, United Kingdom, and other governments should immediately suspend arms sales to Saudi Arabia."
Some are calling on the United States to stop selling arms to Saudi Arabia.
"The United States, United Kingdom, and other governments should immediately suspend arms sales to Saudi Arabia," Human Rights Watch said, calling the attack an "apparent war crime."
"The funeral strike underscores the urgent need for credible international investigations into alleged laws-of-war violations in Yemen," it said.
The US Senate last month rejected a bipartisan proposal to block a pending $1.15 billion arms sale to Riyadh.
Critics of the military deal, which was approved by the Obama administration, complained it could further drag the US into the war in Yemen and contribute to the worsening humanitarian crisis.
The coalition, which involves several Arab countries, started a military campaign in Yemen last year after Houthis took over Sanaa. The crisis quickly escalated into a war that allowed al Qaeda and ISIS -- other enemies of the Houthis -- to thrive amid the chaos.
The conflict has killed about 10,000 Yemenis and left millions in need of aid, according to the United Nations, which has called it a "humanitarian catastrophe."
Since peace talks in Kuwait failed in August, the coalition has intensified airstrikes despite criticism from rights groups that the attacks often hit civilian targets with devastating results.