More than 15,000 people had to leave their homes as hundreds of flights were cancelled and offices and schools shut.
The typhoon packed winds of up to 198km/h (123mph) and made landfall just before 06:00 local time (22:00 GMT Thursday) in eastern Taitung.
The storm is expected to hit China's Fujian province by Saturday morning.
The storm has now weakened to a medium-strength typhoon, according to the island's Central Weather Bureau and should be a tropical storm upon reaching China.
"The wind is very strong," a resident of Taitung told the Reuters news agency.
"Many hut roofs and signs on the streets have been blown away," another resident said.
Some 270,000 households have been affected by power cuts, Li Wei-sen, Taiwan's Central Emergency Operations Center spokesman told news agency AP.
He also added that railway services had been suspended, and more than 500 domestic and international flights cancelled.
Nearly 4,400 soldiers have been deployed around the island, with 35,000 troops on standby to help with evacuations and disaster relief.
A storm is classed as a super typhoon if it reaches maximum sustained 1-minute surface winds of at least 65 m/s (145mph), the equivalent of a category-five hurricane in the Atlantic basin.
Taiwan is often hit by typhoons, with super typhoon Dujuan killing three people and leaving more than 300 injured in Taiwan in 2015.
Typhoon Nepartak hit Taiwan's east coast on Friday, leaving two dead and 66 injured, as well as forcing evacuations and disrupting services.