The quake sent people running into the streets and was also felt in Hong Kong, more than 700 kilometres away.
The tremor at 0543 GMT was centred 32 kilometres east of the central county of Nantou at a depth of 10 kilometres, Taiwan's Seismology Centre said.
The National Fire Agency said a mountain climber was killed after he was hit by falling rocks on Mount Ali in central Taiwan.
TV footage showed landslides, stirring clouds of yellow dust, on other mountains in the area.
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Six high-speed trains halted but services resumed after no damage was found to the line.
"This is the biggest earthquake to hit this year. As the origin of the quake was shallow and it happened in the centre of the island, its velocity could be felt islandwide," Lu Pei-ling, deputy chief of the seismology centre, told reporters.
"Today's earthquake was somewhat related to the 1999 one."
Nantou county was the epicentre of a 7.6-magnitude quake in September 21, 1999 that killed around 2,400 people in the deadliest natural disaster in the island's recent history.
Taiwan lies near the junction of two tectonic plates and is regularly hit by earthquakes.