The USS Barry undertook the so-called "freedom of navigation operation" on Tuesday, a week after Beijing upped its claims to the region by designating an official administrative district for the islands.
The US sought to assert the "rights, freedoms and lawful uses of the sea recognized in international law," the Navy said in a statement.
"Unlawful and sweeping maritime claims in the South China Sea pose an unprecedented threat to the freedom of the seas, including the freedoms of navigation and overflight and the right of innocent passage of all ships," it said.
The move came amid a rise in US-China tensions over the novel coronavirus epidemic, in which Washington has accused Beijing of hiding and downplaying the initial outbreak in December and January in the Chinese city of Wuhan.
The United States rejects China's territorial claim to much of the South China Sea, including the Paracels, also claimed by Vietnam and Taiwan.
The region is believed to have valuable oil and gas deposits.
In a statement on the People's Liberation Army website, the Chinese military said it had mobilized sea and air assets to track and warn the US vessel away from "Chinese territorial waters."
The PLA accused the United States of "provocative acts" that "seriously violated international law and China's sovereignty and security interests."
The US action was "also incompatible with the current joint efforts of international community to fight against the COVID-19," it said.
Last week China sought to further advance its territorial claims when it announced that the Paracel and nearby Spratly islands, the Macclesfield Bank and their surrounding waters would be administered under two new districts of Sansha city, which China created on nearby Woody Island in 2012.
It also announced official Chinese names for 80 islands and other geographical features in the South China Sea, including reefs, seamounts, shoals and ridges, 55 of them submerged in water.
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