Businesses and schools were shut in most southern areas of the island, with 51 people injured.
Television images showed severe floods in parts of the largely rural eastern county of Yilan, with waters neck-deep as soldiers mounted rescue efforts for those stranded.
"The water came in so quickly," said fisherman Hung Chun-yi, who spent the night clearing mud from his home in the eastern harbour town of Suao, after its first floor was engulfed in waters 60cm deep.
"It rained so much, and so fast, the drainage couldn't take it."
The fire department said about 8300 people were moved from their homes to safer areas, mostly in Yilan and nearby Hualien, where a monsoon from the north swelled the rainfall with the unseasonably late typhoon.
Yilan's town of Dongshan received 794mm of rain on Tuesday, weather officials said.
Fung-wong is forecast to graze the far southern tip of Taiwan later on Wednesday before heading into the Pacific Ocean. It lost considerable strength after hitting the the Philippines, where it killed at least 25 people and displaced more than 1.4 million.
A typhoon in September unleashed floods that killed 18 people in Hualien.
Fung-wong will not directly affect the northern city of Hsinchu, home to TSMC, the world's largest contract chipmaker.
