Jangmi is the fourth typhoon to hit Taiwan this year, and is likely to be the most powerful, according to the bureau.
'Super torrential rains'
Local CTI Television showed villagers leaving the mountain resort of Lushan in central Taiwan, which was badly damaged when Typhoon Sinlaku hit two weeks ago, with massive mudslides destroying at least three hotels.
The weater bureau has warned of "super torrential rains" in several mountainous areas.
Taiwan's China Airlines and EVA Airways said several flights to Asia were cancelled or rescheduled for Monday. China's Southern and Hainan Airlines cancelled their flights to the island from Beijing and Shanghai.
After hitting Taiwan, the typhoon was expected to weaken but still carry on northwest to China's Fujian province.
Typhoons frequently hit Taiwan between July and October, causing flash floods and deadly landslides. Typhoon Sinlaku earlier this month killed 12 people and left 10 others missing.