Power outages in many areas have been reported.
Tremors were felt also in mainland China threatening to delay rail traffic in the southwest as workers checked for damage to a local railway, Xinhua news agency reported.
The US Geological Survey said the earthquake was centered 27 miles southeast of Tainan and occurred at a shallow depth of 6.2 miles, which likely amplified its effects.
Located along the Pacific Rim, Taiwan frequently experiences mild to strong earthquakes.
A 7.6 magnitude quake struck the island in 1999, killing nearly 3,000 people and injuring roughly 9,000.