The officials, speaking on condition of anonymity, said the USS John S McCain travelled close to Mischief Reef in the Spratly Islands.
It was the third "freedom of navigation operation" during Trump's presidency.
The operation in the contested waters comes as President Donald Trump's administration seeks Chinese co-operation in dealing with North Korea's missile and nuclear programs and could complicate efforts to secure a common stance. However, the U.S. says its patrols are aimed at showing support for free passage to vessels in worldwide waters.
China's "nine-dash line" - its claimed territorial waters that extend hundreds of miles to the south and east of its island province of Hainan - abut its neighbors' claims and, in some cases, encroach upon them.
"It is clear who is not willing to see stability in the South China Sea and who is the major factor pushing for militarisation in the South China Sea", the spokesperson said.
But Washington's patrols have often angered Beijing because the USA is not a claimant in the territorial dispute in the mineral-rich South China Sea.
McCain on Thursday entered the waters near Mishchief Reef in the Spratly Islands to carry out freedom of navigation operations in the area, reports Efe news.
China's foreign ministry said: "The US destroyer's actions have violated Chinese and global laws, as well as severely harmed China's sovereignty and security".
"And the point of that is to demonstrate that the United States will continue to fly, sail and operate wherever worldwide law allows". It is also believed to be rich in natural resources, including oil.
"But provocative actions by the United States like this one have seriously harmed mutual strategic trust, and caused difficulties and obstacles in developing military-to-military relations".
Geng reiterated that the United States provocation would force China to take further measures to strengthen homeland defense capacity.
"The US destroyer's actions have violated Chinese and global laws, as well as severely harmed China's sovereignty and security", it said.
China's sovereignty claim over the sea has been challenged by five regional nations - Vietnam, Taiwan, Brunei, Malaysia and the Philippines.