The epicentre of the quake, which struck at 0438 GMT on Wednesday, was about three km west of Cheng Kung in Taitung county on the island's southeast coast, at a depth of 10 km, the Central Weather Bureau said in a statement.
Taiwan's interior ministry said the Taitung county government reported no damage except mobile phone service outages.
Tremors could be felt as far as the capital city of Taipei, near the island's northern tip. Taiwan Semiconductor Manufacturing Co (TSMC), the world's largest contract microchip maker, said it saw no immediate damage at its main facilities in northwestern Taiwan's Hsinchu.
Workers were not evacuated and no power outage occurred, a TSMC official said. Flat computer screen makers AU Optronics and Chi Mei Optoelectronics also said their manufacturing plants were operating normally.
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 Richter scale, it killed more than 2400 people and destroyed or damaged 50,000 buildings.