The earthquake struck at a depth of about 5km, and was the biggest to hit the Kaohsiung area in recent years, the weather bureau reported.
Officials in Jiashian told local media that there was a small landslide in an uninhabited area.
Services on the Kaohsiung subway were also halted, as were trains on the high-speed rail connecting the north and the south of the island, television reports said.
In the city of Nantou, in the south of the island, water and power lines were cut.
Taiwan is regularly hit by earthquakes as the island lies near the junction of two tectonic plates.
In September 1999, a 7.6 magnitude earthquake killed around 2,400 people in the deadliest natural disaster in the island's history.
Most modern buildings in Taiwan are built to withstand earthquakes.