Wanying Zhang, also know as Heather, surveilled the Taiwanese president's son and his family for the Chinese government while in the United States, according to the FBI.
Zhang, 34, was arrested on charges for working for China as an unregistered agent, Assistant US State Attorney Bill Essayli announced on social media.
Zhang took photos and videos of her targets and sent number plate information to Chinese officials, he said.
Zhang was arrested as she was departing for a flight to China.
Her nationality was not clear, and a lawyer who represents her could not be determined.
She was due to appear on Monday in federal court in Los Angeles.
Taiwan's Presidential Office confirmed President Lai Ching-te's relatives were the targets, without specifying if it was the president's son, saying that "this is a classic case of transnational repression".
"Taiwan condemns in the strongest terms such barbaric acts - which disregard human rights and national sovereignty and aim to suppress, threaten, or even harm individuals advocating for freedom and democracy or their families - as such behaviour should not be tolerated in the civilized world," spokeswoman Karen Kuo said in a statement.
The Chinese embassy in the US did not immediately respond to a request for comment Monday and the foreign ministry in Beijing was closed for holidays.
Taiwan and China split after a civil war in 1949, but Beijing claims the island as part of its own territory.
Lai, who was voted into office in 2024, has said that Taiwan and Beijing do not belong to each other and that the "People's Republic of China has no right to represent Taiwan".
China considers him a separatist and has called him a "destroyer of peace".
While in office, Lai has stepped up spending on defence for Taiwan, notably pledging to increase defence spending from three per cent to five per cent of GDP, and pushing through a special budget for the construction of a T-Dome air defence system.
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