Vietnam, China, and Taiwan all have overlapping claims in Paracel Islands.
"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.
The Chinese spokesperson said the United States warship violated Chinese and worldwide laws and seriously threatened China's sovereignty and security.
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".
She also said that China already lodged a protest to the United States government.
Expressing firm opposition to the USA move, Hua said China will continue to take resolute measures to protect its territorial sovereignty and maritime interests.More news: Budget 2018: Main Points So Far
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"China will continue to take resolute measures to protect Chinese sovereign territory and maritime interests".
Next month, Trump makes his first visit to Asia as president, including a stop in China, which he has been pressuring to do more to rein in North Korea.
The destroyer, however, did not violate the 12-nautical-mile territorial limits of the islands, according to a Reuters report, citing USA military officials.
Beijing condemned the mission of the guided-missile destroyer USS 'Chafee, ' which on Tuesday sailed within 16 nautical miles of the disputed Paracel Islands in the South China Sea, within the framework of a so-called "freedom of navigation" operation.
That agreement was signed after a U.S. destroyer sailed near a man-made island constructed by China as part of another "freedom of navigation" operation meant to challenge Beijing's territorial claims. "China urges the U.S.to conscientiously respect China's sovereign territory and security interests, conscientiously respect the efforts regional countries have made to protect peace and stability in the South China Sea, and stop these wrong actions".