Typhoon Gaemi, packing sustained wind speeds of 162 kilometres (100 miles) per hour, also affected Japan and the Philippines -- which also announced that government offices would close for the day.
It is expected to make landfall in northeast Taiwan by 10 pm (1400 GMT), and President Lai Ching-te urged everyone to "put safety first" during a morning emergency briefing.
"Gaemi is this year's first typhoon to make landfall in Taiwan," Lai said.
"I hope that through our joint efforts, impact from the typhoon can be minimised... I also encourage fellow citizens across the country not to go out unless necessary during the typhoon, especially not to dangerous places."
The weather forced the self-ruled island to cancel some of its annual Han Kuang war games -- which test preparedness for a Chinese invasion -- but an anti-landing drill went ahead as scheduled on Wednesday morning on Penghu island, west of Taiwan.
Authorities evacuated more than 2,100 people living in precarious conditions in three northern regions, particularly Hualien -- a mountainous area with high risk of landslides.
Trains and ferry services were suspended and more than 250 international flights were cancelled on Wednesday.
"We expect that the impact of the typhoon will be extended to four days (until Friday)," said Taiwan's Central Weather Administration chief Cheng Jia-ping, adding that the public would need to "take precautions against heavy rain and strong wind".
Massive waves crashed against the coast of northeastern Yilan county and, in the capital Taipei, shops and government offices were closed.
Student Ray Su said he was "very happy" that he didn't have to go to cram school -- a specialised centre that tutors students.
"When the teacher announced the typhoon holiday last night, the whole class cheered," Su told AFP, adding that he was "not too worried" about the typhoon's impact.
Taiwanese chip giant TSMC, the world's largest contract chipmaker, said it will maintain normal production and the firm "has activated routine typhoon alert preparation procedures" at all fabrication plants.
Taiwan is accustomed to frequent tropical storms from July to October, but experts say climate change has increased their intensity, leading to heavy rains, flash floods and strong gusts.
In neighbouring Japan, authorities of a southern island region of Okinawa urged residents to "exercise strong vigilance" against storms, high waves and floods.
In the Philippines, meanwhile, heavy downpours in Manila triggered widespread flooding and a landslide in a nearby mountainous province killed four people.
burs-dhc/fox
