The U.S. Geological Survey said on its website (www.usgs.gov/) the quake had a magnitude of 6.4 and was centred just off the island's east coast, 25 km (15 miles) south-southeast of the city of Hualien.
There were no reports of tsunami warnings being issued.
Early television reports that a building had collapsed near Taipei were not correct, a Taiwanese disaster agency said.
At least four people were hurt during the quake, Taiwanese television reported later. A water tower collapsed and glass shattered in a hotel, it said, while two roads were cut outside the capital.
TSMC, the worlds largest contract chipmaker, reported no damage at its Taiwan facilities.
The quake was recorded at 9.02 pm local time (1:02 p.m. British time) and was centred 44 km (27 miles) below the surface, Taiwan's Central Weather Bureau said.
Earthquakes occur frequently in Taiwan, which lies on a seismically active stretch of the Pacific basin.
One of Taiwan's worst-recorded quakes occurred in September 1999. Measuring 7.6 on the old Richter scale, it killed more than 2,400 people and destroyed or damaged 50,000 buildings.
(Reporting by Ralph Jennings; Editing by Paul Tait)