The quake hit 34 kilometres (21 miles) east-southeast of Taitung City at 11:52 pm (1552 GMT), the US Geological Survey said.
Taiwan's Central Weather Bureau measured it at a stronger 6.0 magnitude at a depth of 20 kilometres.
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The quake caused short power outages and toppled goods from shop shelves, photographs posted on the Central News Agency website showed, but there were no reports of major damage.
Taiwan lies near the junction of two tectonic plates and is regularly hit by earthquakes.
A 6.4-magnitude earthquake in February left 117 dead when an apartment complex collapsed in the southern city of Tainan.
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