China claims sovereignty over democratically governed Taiwan, and says it has jurisdiction over the strait.
The US Navy's 7th Fleet said in a statement that the destroyer USS Ralph Johnson made a "routine" transit of the strait in accordance with international law, Reuters reported.
China's military described the sailing as "public hype", adding it had sent naval and air forces to monitor and warn the US ship and "deal with it in accordance with the law and regulations".
"Troops in the theatre remain on high alert at all times and will resolutely safeguard national sovereignty and security as well as regional peace and stability," the Eastern Theater Command of the Chinese People's Liberation Army said.
Taiwan's defense ministry said the ship sailed in a northerly direction through the strait and that Taiwanese forces had monitored the situation but observed nothing unusual.
US military ships and aircraft transit the narrow strait about once a month.
Taiwan's government rejects China's sovereignty claims and says only the island's people can decide their future.
China has never renounced the use of force to bring Taiwan under its control.