The incident involving the USS McCampbell occurred as the US and China begin trade talks.
A spokeswoman for the US Pacific Fleet, which is responsible for security in the Indo-Asia-Pacific, said the US destroyer was carrying out a "freedom of navigation" operation in the region and was not political.
Chinese Foreign Ministry spokesman Lu Kang said Chinese military aircraft and naval vessels were dispatched to identify the US vessel and warn it to leave the area near disputed islands in the South China Sea.
"We have made stern complaints with the US," Mr Lu said.
He said the warship, which he said was the destroyer the USS McCampbell, had violated Chinese and international law, infringed on Chinese sovereignty and undermined peace and stability. He said:
"We urge the United States to immediately cease this kind of provocation."
He went on to say: "As for whether this move has any impact to the ongoing China-US trade consultations... to properly resolve existing issues of all kinds between China and the US is good for the two countries and the world."