The ship entered the strait on Thursday and sailed in a southerly direction, the ministry said.
"During the passage through the strait, Taiwan's military monitored the situation of the sea and air space, and the situation was normal," it said.
The 180-kilometre (110-mile) strait is a major shipping route, but also serves as a tense geopolitical tussling ground for Beijing -- which claims democratic Taiwan as its territory.
Taiwan's military reports near-daily sightings of vessels around its waters, as well as incursions made by Chinese warplanes in its air defence zone.
The United States sends its warships through the Taiwan Strait for "routine" transits, and British, Canadian, French and Australian warships have all made passages in recent years -- sparking protests from Beijing.
Thursday's strait passage was made by Australia's HMAS Toowoomba, which was transiting international waters as part of its regional deployment.
Asked about the transit, Beijing's foreign ministry said its position was "clear and consistent".
"We urge the relevant parties not to take provocative actions to create trouble for peace and stability in the Taiwan Strait," spokesperson Mao Ning said.
The long-range frigate was in waters off Japan earlier this month, supporting United Nations sanctions enforcement efforts within Tokyo's exclusive economic zone.
But navy divers from the HMAS Toowoomba were injured, "likely" from sonar pulses emitted by a Chinese warship, Australia's defence minister said last week.
Beijing called Canberra's accusation "reckless and irresponsible", while Australian Prime Minister Anthony Albanese said the Chinese warship had displayed "dangerous... and unprofessional" conduct at sea.
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