The quake struck at 4:06 am (20:06 GMT) about 25 kilometres (15 miles) east of Taitung City in the island's southeast, the United States Geological Survey (USGS) said.
The epicentre of the quake, which hit at a depth of 25 km, was located about 110 km east of Kaohsiung, Taiwan's second largest city and a major port hub, USGS said.
The island lies near the junction of two tectonic plates that is regularly hit by earthquakes.
A strong 6.3-magnitude quake which hit central Taiwan in June last year killed four people and caused landslides.