China, which considers Taiwan its territory, was outraged by massive support for the island from the Trump administration, such as increased sales of arms.
Fallout from the coronavirus pandemic and trade tensions have also buffeted relations between Beijing and Washington.
The defense ministry of Aiwan said that the ship was heading south on what it called the "ordinary mission," adding that it proceeded in that direction.
In recent months, both China and the US have ramped up military activities near Taiwan, including regular U.S. sailing through the Taiwan Strait, and regular Chinese air force drills near the island.
Last Friday, Taiwan said a Chinese Y-8 air force had momentarily crossed into the Air Defense Identification Zone in Taiwan, causing Taiwan jets to alert it to leave.
China uses the Y-8 both as a transport and as an aircraft for early warning and electronic warfare.
Taiwan criticized the Chinese exercises as attempts at coercion and advised Beijing that instead of intimidating the island, it would focus its attention on combating the coronavirus.
China views Tsai as a separatist, an argument which she firmly rejects.
Maritime Business World