Both missiles hit the water before reaching the USS Mason, a guided-missile destroyer.
A spokesman for Yemen's rebel Houthi movement told the Saba news agency that it had not targeted any warships.
The incident came eight days after an attack on an Emirati civilian ship that was also blamed on the Houthis.
The UAE government said the high-speed catamaran was carrying aid, wounded Yemenis and passengers when it was hit in the Bab al-Mandab strait.
US Naval Forces Central Command spokeswoman Paula Dunn said in a statement on Monday that the USS Mason had been "conducting routine operations in international waters" north of the strait when it "detected two inbound missiles" around 19:00 (16:00 GMT) on Sunday.
"Both missiles impacted the water before reaching the ship," Ms Dunn said, adding that "there were no injuries to our sailors and no damage to the ship".
"We assess these missiles were launched from Houthi-controlled territory."
However, a Houthi military spokesman told Saba that the charge was "baseless and aimed to cover for the heinous Saudi crime of Saturday's air attacks on the civilian funeral hall in the capital Sanaa", which killed more than 140 people.
A Saudi-led multinational coalition, whose air campaign against the Houthis and their allies is supported by the US, has denied any responsibility.
Also on Monday, the coalition said it had intercepted a ballistic missile fired by the Houthis at the King Fahd Air Base in Taif in central Saudi Arabia, which hosts US military personnel training the kingdom's armed forces.
A missile was also reportedly fired at the Yemeni government-controlled city of Marib in central Yemen.
The UN says at least 4,125 civilians have been killed and 7,207 injured since the coalition intervened in the conflict between forces loyal to Yemen's internationally-recognised government and those allied to the Houthis in March 2015.
Two missiles were fired at a US warship from rebel-held territory in Yemen as it passed through the Red Sea on Sunday, the US Navy has said.