Dozens of flights and ferry services were cancelled, while several highways across the island were shut amid fears of landslides and floods.
A typhoon will hit northern Taiwan later on Monday, meteorologists said, shutting financial markets and schools as airlines cancelled dozens of flights amid warnings of floods and high winds on the island.
Typhoon Mitag, categorised by Taiwan's weather bureau as the second-strongest typhoon level, was expected to approach the coast of the northeastern county of Yilan with maximum winds of 162 kmh (100 mph).
It was moving across the ocean in a north-northwesterly direction at 27 kmh (17 mph), weather officials said, and could gain strength as it approaches the island.
The bureau issued wind and rain warnings for greater Taipei, the northern port city of Keelung, and other northern counties. It also put out a warning to seafarers around Taiwan.
"Typhoon Mitag is about to hit Taiwan ... Please pay attention to your safety and make preparations for the typhoon," Premier Su Tseng-chang wrote on Facebook late on Sunday.
The typhoon was expected to approach China's eastern city of Shanghai on Tuesday, forecasts showed.
Typhoons regularly hit Taiwan, China, the Philippines and Japan in the second half of the year, gathering strength from the warm waters of the Pacific Ocean or South China Sea.
Typhoon Morakot devastated Taiwan in 2009 and killed nearly 700 people, most of them in landslides.