The Paracel Islands have been controlled by China since 1974 but they are also claimed by Vietnam and Taiwan.
"China immediately sent naval vessels and military jets to investigate and identify, as well as warn to the vessel and ask it to leave", Hua said in a daily news briefing.
South Korea's new ambassador to China said Tuesday conflict between the two countries over Seoul's deployment of a Terminal High-Altitude Area Defense battery from the US "cannot continue this way".
Chinese foreign ministry spokeswoman Hua Chunying on Wednesday denounced the mission as risky and a violation of China's sovereignty.
The incident with the USS "Chafee" would affect trust between the militaries of the two countries, the ministry stated, adding that further operations of such nature might trigger "unwanted incidents".
China is protesting the sailing of a US Navy ship near its territorial claims in the South China Sea, saying it will continue to take measures to protect Beijing's interests in the vital waterway claimed by several nations.
"It is a critical stage for the development of the relationship between Chinese and American armies, and we demand the USA side earnestly take steps to correct its mistakes", the ministry said. Beijing accuses the U.S. of violating its sovereignty, while Washington claims the missions support "freedom of navigation" in the region.
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The destroyer, however, did not violate the 12-nautical-mile territorial limits of the islands, according to a Reuters report, citing United States military officials. China is North Korea's neighbor and biggest trading partner.
China has lodged a representation with the United States after a US destroyer intruded into China's territorial waters in the South China Sea.
Twelve nautical miles mark internationally recognized territorial limits.
Experts and some USA officials have criticized former president Barack Obama for potentially reinforcing China's claims by sticking to innocent passage, in which a warship effectively recognized a territorial sea by crossing it speedily without stopping.
China claims the South China Sea and its islands virtually in their entirety.