The Netherlands said the frigate was operating in accordance with international law.
Zhai Shichen, a spokesman for the People's Liberation Army Southern Theatre Command, said in a statement that carrier-based helicopters had repeatedly taken off and "intruded into China's airspace".
"We firmly oppose this and solemnly urge the Dutch side to immediately cease its infringing and provocative acts," Zhai said, adding the Chinese military will resolutely safeguard national sovereignty and security.
In a statement, the Netherlands said that HNLMS De Ruyter was sailing through the South China Sea for diplomatic, security and economic reasons.
It declined to comment on operational details.
The Chinese claim marks a relatively unusual public confrontation with the Netherlands in the South China Sea.
China claims almost the entire South China Sea, including parts also claimed by Brunei, Indonesia, Malaysia, the Philippines and Vietnam.
In 2016 the Permanent Court of Arbitration in The Hague ruled that China's claims were not supported by international law, a decision that China's government rejected.
