The ground floor of the Marshal Hotel in Hualien county caved in, causing the death of one employee.
Efforts to rescue people trapped inside is underway.
Meanwhile, no tsunami warning has been issued as result of natural disaster.
A magnitude 6.4 quake struck near the coastal city of Hualien in Taiwan late on Tuesday, the U.S. Geological Survey (USGS) said, killing at least two people and causing several buildings to collapse.
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A group of Kiwis caught up in the magnitude-6.4 Taiwan natural disaster ran from their hostel and straight for higher ground.
The quake was centered in the East China Sea about 21 kilometers north-northeast of Hualien City.
Officials had no numbers for missing people.
Rescuers are seen entering damaged buildings after the quake. Today's quake occurred on the second anniversary of another that killed 117 two years ago.
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"We live in Wellington and we have experience a few but this is definitely so much bigger", she said. We dare not go back home now. "I wouldn't be surprised for there to be a number of aftershocks in the next couple of days". According to initial reports, heavy damage has been reported after the strong quake hit Taiwan coast.
On Sunday, another five shallow tremors struck within two hours of each other in the same area off Taiwan's east coast.
The Hualien Shangxiao Road Community Apartment suffered severe damage and was tilted 45 degrees, the first and second floors nearly completely crushed, Taiwan News reported.
On Sunday an natural disaster with a magnitude of 6.1 struck nearby.
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