Haikui made landfall in the mountainous and sparsely populated far southeast of Taiwan mid-Sunday afternoon, the first typhoon to directly hit Taiwan in four years. Counties and cities in the region cancelled classes and declared a day off for workers.
Taiwan President Tsai Ing-wen told a meeting of disaster management officials that people should avoid going out and not go up mountains, to the coast, fishing or engage in water sports, according to a statement from her office.
The fire department said two people were slightly injured when a tree fell on a truck in the eastern county of Hualien. There were few other reports of damage. In the capital Taipei there were only sporadic rain showers.
According to the weather bureau, Haikui was registering maximum sustained winds of about 150km/h with gusts of up to about 190km/h.
Haikui is a much weaker storm than Typhoon Saola which hit Hong Kong and the southern Chinese province of Guangdong on Saturday.
Taiwan's government said that 3729 people had been evacuated, mainly in the south and east.
Taiwanese airlines cancelled all domestic flights on Sunday, while ferry services to surrounding islands were also suspended.
There was less disruption to international flights, with only 41 cancelled for Sunday, the Civil Aeronautics Administration said.
The military has mobilised soldiers and equipment to help with flood relief and evacuation efforts.
After passing across southern Taiwan, Haikui is forecast to enter the Taiwan Strait and head towards China.
with agencies
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