The People's Republic of China condemns any official contact with the island, which functions as a sovereign political entity.
The minister arrived at 04:48 (local time, minus seven in Lisbon) at Songshan airport, in the capital of Taiwan.
Azar's agenda does not include official activities until Monday, when he will meet with Taiwanese President Tsai Ing-wen.
On the same day, the US Secretary of Health will also visit the disease control center, accompanied by Taiwan's Minister of Health and Welfare, Chen Shih-chung.
On Wednesday, Alex Azar is expected to speak at the University of Taipei.
This visit represents another step in Washington's current policy of rivalry with China on virtually all fronts: trade, technological competition, the new coronavirus pandemic, human rights or the South China Sea sovereignty.
The Taiwan issue is seen by Beijing as the "most sensitive and important" in its relationship with the United States.