UPDATE: A second person has been pronounced dead.
The U.S. Geological Survey said on its website that the 6.5-magnitude temblor hit at 1:43 p.m. local time, 15 miles south-east of Buli in Nantou county, and at a depth of 9 miles.
Buildings shook for almost a minute in the capital of Taipei, about 150 miles north of the epicenter, and people over 400 miles away in Hong Kong reported feeling the tremor.
Taiwan television reported that the quake caused a gas explosion in the center of the island.
A man who was mountain climbing on Mount Ali in central Taiwan died after being struck by falling rocks, according to AFP.
One TV reported that several people were seriously injured in Zhushan Township and had to be rushed to hospital.
In March, a 6.0-magnitude earthquake hit Nantou county, reportedly killing one and injuring nearly 100.
In 1999, over 2,300 people perished after a 7.6-magnitude quake struck Taiwan, also in Nantou county.