The U.S. Geological Survey said the earthquake measured magnitude 6.6 and struck in the evening. It was centered in a remote mountainous area 45 kilometers (28 miles) south-southwest of the coastal city of Hualian at a depth of just 9.3 kilometers (5.8 miles), it said.
In Taipei, the capital, buildings swayed for more than 10 seconds and startled residents ducked for cover.
Local TV channels reported that there appeared to be almost no damage in Hualian. However, it could take some time for the full impact of the quake to be evaluated because of the remoteness of the epicenter.
Earthquakes frequently rattle Taiwan, but most are minor and cause little or no damage.
However, a magnitude-7.6 earthquake in central Taiwan in 1999 killed more than 2,300 people.