This is considered the latest in a series of maritime attacks targeting transport routes in the area related to the Israel-Hamas war.
AP said that in a statement issued by the Department of Defense, US officials did not immediately determine the origin of the attack.
Immediately afterwards, the Iran-backed Houthi rebels in Yemen said that two ships with ties to Israel were attacked by the country's forces with drones and missiles, but did not admit to targeting the US Navy ship.
We have heard of reports of attacks on the US Navy Carney and commercial vessels in the Red Sea and will provide information as soon as it is available, the Pentagon said in a statement to AP.
The US Department of Defense did not specify the damage (if any) to the Arleigh Burke-class destroy ship during the attack.
Earlier, on the same day, December 3, the UK's Maritime Trade Commission said it had learned about the drone attack in the Babel-Mandeb Strait in the Red Sea.
The agency also said that the drone originating from Yemen was operating in the area and that an explosion could have occurred.
A series of maritime attacks have been reported in the Middle East as the war between Israel and Hamas risks leading to a wider regional conflict.
Last month, Houthi rebels seized a transport ship linked to Israel in the Red Sea off the coast of Yemen.
The Houthi rebels have previously fired ballistic missiles and armed drones at Israeli targets and said they will continue to target Israeli ships in the area.
Yemeni armed forces continue to block Israeli ships from moving in the Red Sea (and the Gulf of Aden) until Israel's aggressive actions against our steadfast brothers in the Gaza Strip stop, Houthi spokesman Major General Yahya Saree said in a statement claiming responsibility for the attacks on December 3.
Mr. Saree also warned: "All Israeli ships or ships related to Israel will become legal targets if they violate what is stated in this statement." He did not mention US warships in the statement.
According to the Navy Times, the USS Carney shot down an Iranian-made drone heading towards its location from Yemen-controlled territory.
The incident occurred one day after another Iranian drone approached the Dwight D. Eisenhower aircraft carrier within a radius of 1,400 m in international waters of the Arabian Gulf.
