By 10 p.m. (1400 GMT) Friday, the eye of the typhoon was 40 km southeast of Hualien on the east coast.
Moving at 11 km per hour (kmph) in a northeasterly direction, it was packing centre winds of 144 kmph and gusts of 180 kmph.
If it maintains its course and speed, Morakot is expected to cross the Taiwan Strait and slam into China's southeast coast Saturday night or Sunday morning, the Central Weather Bureau said.
Morakot however is expected to weaken after crossing Taiwan.
The typhoon cut off power to about half a million homes and paralyzed Taiwan's road and air traffic.
On Friday, 144 domestic flights and 255 international flights were cancelled while several takeoffs were delayed.
Taiwan has declared Friday a 'typhoon holiday' to prevent typhoon-related accidents. Several counties and cities said they will continue to have a typhoon holiday Saturday despite Morakot's expected departure.