Tembin, characterised as a "severe" typhoon by the Hong Kong Observatory, reached the southern county of Pingtung at 5:00 am (2100 GMT Thursday), Taiwan's Central Weather Bureau said.
Toppled trees covered roads in the south, and in the coastal village of Tawu a number of rooftops were reportedly blown off by strong winds.
Police have set up roadblocks in several locations leading into areas considered in danger of landslides, only letting through those on urgent business.
About 5,000 people have been evacuated from risk areas along Taiwan's mountainous coastline as authorities attempt to prevent a repeat of an enormously destructive typhoon which hit three years ago.
Typhoon Morakot killed about 600 people in August 2009, most of them buried in huge landslides in the south.
What the stars mean:
★ Poor ★ ★ Promising ★★★ Good ★★★★ Very good ★★★★★ Exceptional