The quake struck at 1811 hrs with its epicentre 32.6 kilometres north-northwest of Hualien county in the east, at a depth of 10 kilometres.
Tremors could be felt by residents on many parts of the island, the centre said.
A strong 6.2-magnitude quake struck the island on June 3 leaving two dead and 21 injured, which was also felt in Hong Kong, more than 700 kilometres away.
Taiwan lies near the junction of two tectonic plates and is regularly hit by earthquakes.