The undersea quake hit at 16:00 local time (0800 GMT) about 44 kilometres southeast of Taitung city in the southeast, at a relatively shallow depth of 17 kms, the US Geological Survey said.
Taiwan's Seismology Centre measured the quake at 5.9-magnitude.
Buildings in the Taipei swayed and the quake was felt across the island but the National Fire Agency said there were no casualties or damage.
Taiwan is regularly hit by earthquakes as the island lies near the junction of two tectonic plates.
In September 1999, a 7.6-magnitude tremor killed around 2,400 people in the deadliest natural disaster in the island's recent history.
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