Images posted online appear to show the first floor of the hotel severely damaged, with parts of the building crumbling onto the sidewalk.
The island's weather bureau recorded the quake as 6.0-magnitude.
Hualien is a popular tourist destination on Taiwan's eastern coast and home to about 100,000 people.
Lai said the government was urgently repairing a major highway damaged by the quake.
Emergency services were working to free three people trapped in the toppled Marshal Hotel. People can be seen running down the street, carrying ladders to climb over the rubble and reach people still inside the collapsed building.
The ground floor of the Marshal Hotel in Hualien county caved in, causing the death of one employee.
The quake's centre was about 20 kilometres east-northeast of Hualien, according the U.S. Geological Survey.
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Two bridges in Hualien City were damaged and sealed off from the public.
It was the only high-rise in Tainan to crumble completely in the quake, which came two days before Lunar New Year, when many people would have been visiting relatives for the biggest celebration of the Chinese calendar.
A magnitude-6.4 natural disaster has rocked Taiwan's east coast, following a "swarm" of 19 earthquakes over the past 48 hours.
Since February 4, about 100 sensible earthquakes have jolted the area.
Meanwhile, media reports said that a hotel has collapsed after the natural disaster hit Taiwan's east coast on Tuesday.
The island's worst tremor in recent decades was a 7.6 magnitude quake in September 1999 which killed around 2,400 people.