Taiwan's weather agency, which put the magnitude at 7.0, said the quake hit at 11:05 pm (1505 GMT) at a depth of 73 kilometres (45 miles) in the sea off Yilan county, southwest of Taipei.
The Yilan County Fire Bureau told AFP there were no immediate reports of casualties or damage.
The quake caused buildings in the capital Taipei to sway, and local media said it was felt across Taiwan.
It also temporarily disrupted electricity supply in a Yilan town, said the National Fire Agency, adding no major damage was reported.
Taiwan Railway said it suspended four trains operating in Yilan, affecting more than 270 passengers.
Taipei's metro lines were running at reduced speed for around 20 minutes until no abnormalities were reported in the stations and tracks, authorities said.
Premier Cho Jung-tai urged the public to "remain vigilant and be mindful of the safety of your neighbours" in a statement issued after the quake.
"A strong earthquake struck an hour ago (23:05). After repeatedly checking the situation in various locations, thankfully, there were only minor incidents," he said in a separate post on Facebook.
Taiwan is frequently hit by earthquakes due to its location on the edge of two tectonic plates near the Pacific Ring of Fire, which the USGS says is the most seismically active zone in the world.
On Wednesday, a 6.0-magnitude tremor struck the island's southeast.
In April 2024, a 7.4-magnitude earthquake killed 17 people as it triggered landslides and severely damaged buildings around Hualien city.
Officials at the time said it was Taiwan's strongest quake in 25 years.
It was the most serious in Taiwan since a 7.6-magnitude tremor struck in 1999 -- the deadliest natural disaster in the island's history.
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