Dujuan was upgraded to a "strong typhoon" on Sunday - also known as a "super typhoon" by some weather agencies. The storm intensified as it approached Taiwan, with gusts of 227 kilometres (141 miles) per hour.
Around 3,000 people, mostly tourists, were evacuated from Taiwan's Green Island and Orchid Island on Sunday, with around 4,000 more moved from other vulnerable areas on Monday. High-speed rail services in the west were also cancelled.
Authorities have warned that coastal areas could be flooded because tides are affected by the current "supermoon" - a rare astrological event in which the moon appears brighter and larger. The moon has reached its closest orbital point to Earth and therefore has a stronger gravitational pull than usual.
In August, Typhoon Soudelor, the most powerful storm of the season so far, killed at least eight people in Taiwan and a further 26 in China. Dujuan is also expected to head across the Taiwan Strait and strike the coast of the south eastern Chinese province of Fujian on Tuesday. By that stage, its winds are likely to have lost much of their force, but torrential rains will still pose a risk in the densely populated region.