The stock market was closed for the day, along with all schools and offices in Taiwan, railway traffic was halted and many flights were cancelled as winds of up to 144 kilometres (90 miles) per hour blew across, uprooting trees.
Hundreds of residents were evacuated from an eastern village threatened by flash floods before the typhoon made landfall in the eastern county of Hualien at 6:50 am (2250 GMT), television images showed.
The National Fire Agency, which coordinates the country's rescue missions, said no casualties were reported as yet.
President Ma Ying-jeou visited a contingency committee outside Taipei which is monitoring the storm, urging residents to be on their guard especially for heavy rainfall.
"We must continue to keep a high vigilance," he said.
Rainfall in the northeast was being measured at nearly 700 millimetres (27 inches).
At 0000 GMT, the eye of the typhoon was around 50 kilometres southwest of Hualien. Forecasters expected it to cut across the island