The quake struck at 3:54 pm (0754 GMT) with its epicentre 87.5 kilometres southeast of the northeastern city of Yilan at a depth of 83.1 kilometres, the central weather bureau 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.