The quake hit at 22:19 local time (1419 GMT), USGS said, at a depth of 190 kilometres (120 miles).
No tsunami warning was issued but Twitter users as far away as Kaohsiung, on the southwest of the island, reported feeling tremors.
Alaska hit by 6.8-magnitude earthquake
China's Earthquake Networks Center put the magnitude higher at 6.2, according to state news agency Xinhua.
Last year one man died and another was hospitalised after a fire caused by a powerful quake off Taiwan set buildings shaking in the capital Taipei and sparked a short-lived tsunami warning in far southwestern Japan.
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