The quake struck at 8:21 am (0021 GMT) with its epicentre 33.3 kilometres (21 miles) southwest of the eastern city of Hualien, at a depth of 18 kilometres, the centre said.
Residents on many parts of the island felt tremors, it said.
The island lies near the junction of two tectonic plates and is regularly hit by earthquakes.
A strong 6.3-magnitude quake which hit central Taiwan in June last year killed four people and caused widespread landslides.
A 7.6-magnitude quake struck the island in September 1999 and killed around 2,400 people.