'Taiwan is an inalienable part of China,' and that China would not tolerate any interference in what it called its internal affairs, said the defence ministry on its website.
A statement posted on the ministry's website called the move provocative and said it shows that the United States is the biggest threat to peace and stability and creator of security risks in the 100-mile wide Taiwan Strait.
'We express firm opposition and strong condemnation,' the statement said.
The USS Kidd guided-missile destroyer and USCG cutter Munro sailed through the strait in international waters, the US Navy said. Such exercises are seen as a warning to China, which recently conducted drills near Taiwan and has not renounced the use of force if needed to bring the island under its control.
'The ships' lawful transit through the Taiwan Strait demonstrates the US commitment to a free and open Indo-Pacific,' a statement from the Navy's Japan-based 7th Fleet said.
The USCG has been stepping up its presence in Asia, as the Chinese coast guard patrols near disputed islands that both China and other governments claim in the South and East China Seas.
The US and Taiwan coast guards held talks this month after the two signed a cooperation agreement in March. China has denounced the agreement.