The US Seventh Fleet later confirmed the information, describing the move as a "routine" transit of the USS Shiloh.
The passage came five days after the island's China-skeptic president, Tsai Ing-wen, won a landslide re-election victory.
"Our determination to safeguard national sovereignty and territorial integrity is rock-solid and we will not permit any person, any organisation, any political party, at any time, by any method to break away any part of China", he added.
The narrow Taiwan Strait which separates the island from China is a frequent source of tension. Anti-China Sai has actually obtained once more in Taiwan within the last few presidential election held on Saturday.
Taiwan denounced this as an attempted intimidation. The USS Shiloh, a US ship equipped with missiles, passing through this sea area is considered as no less than a warning to China.
A USA warship sailed through the Taiwan Strait, after President Donald Trump signed a trade deal with China and Taiwan reelected a leader seeking greater American military support to counter a threat from Beijing.
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Despite the lack of formal diplomatic ties, United States law requires Washington to ensure Taiwan has the means to defend itself.
It can also be becoming known as an United States demonstration in help of President Sai Ing-wen, which preferred the island's autonomy into the recently determined election in Taiwan.
"As a responsible member of the worldwide community, Taiwan will continue to dedicate itself to protecting peace and stability in the Taiwan Strait", the presidential office cited Tsai as telling Catherine Nettleton. If the US-China relationship recovers - as could be the case this week's trade deal - or Trump wants to do a favor for his "friend" Xi, that engagement could weaken.
Mr Christensen, director of the American Institute in Taiwan, said: "Perhaps this concept sounds simple, but it is important to consider its significance within the current context".
Earlier on Friday, U.S. diplomat William Brent Christensen, who is director of the American Institute in Taiwan, said at a forum in Taipei that the U.S. this year will seek to further Taiwan's engagement in the world, accusing Beijing of blocking Taiwan's participation in most global organizations.