The agency also posted photos showing a road fractured in several parts.
Some 88 soldiers were helping the local fire service respond at the hotel, and another 250 were on standby to help.
The Central Weather Bureau reported at least three strong aftershocks following the first, which struck at 23:50pm.
The quake is the largest in the series that has rocked the east coast of Taipei since late Sunday evening, with a series of smaller temblors rattling the area continually over the course of the last few days.
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.
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According to some reports a Hotel collapsed after the tremors.
The quake took place at a depth of 1km (0.6 miles), the report says.
Facebook user Sun Chen-hsiang, who was livestreaming the scene at the hotel from a distance, told how the building next to his home had collapsed.
Taiwan's natural disaster experts said more quakes might happen in the coming weeks.
Gas leaks, blackouts and rockfall were also reported.
A series of earthquakes is rocking Taiwan, leaving two dead and more than 100 injured, according to The Associated Press, which cites Taiwan's premier, William Lai.
The quake follows a 6.1 magnitude quake off the coast of Hualien on the east of Taiwan, which lies along the Pacific Rim of Fire.