The storm brought "destructive" gusts of up to 222 kilometres (138 miles) per hour to southwest Taiwan, where it made landfall late Sunday, the Central Weather Administration said.

"This was the first time on record that a typhoon made landfall in Chiayi (county), it was a very unusual path," the forecaster from the weather agency said.

The storm moved northward near Taiwan's west coast overnight and left Taiwan early Monday morning, but extremely heavy rain continued.

At least 491 people have been treated for injuries, according to the National Fire Agency.

A 60-year-old man died after a power outage at home caused his ventilator to stop functioning and a 69-year-old man was killed by a fallen tree when driving, the agency said.

The storm caused widespread power outages across Taiwan, affecting around half a million households, it said. Nearly 400,000 homes remained without power on Monday morning.

Danas dumped more than 500 millimetres (20 inches) of rain across southern Taiwan over the weekend, the weather agency said.

Nearly 3,500 people were evacuated from their homes, mostly in mountainous areas around the southern port city of Kaohsiung, firefighters said.

Thirty-three international flights from Taiwan were cancelled on Monday.

Taiwan is accustomed to frequent tropical storms from July to October.