The quake struck about 22 kilometres north-east of Hualien shortly before midnight, and the epicentre was very shallow at just one kilometre, the USGS said.
The lower basement and ground floor of the 10-storey Marshal Hotel gave way.
“Two people were unfortunately killed, and 114 have suffered light or severe injuries,” Taiwan’s Premier William Lai told an emergency government meeting.
At least 28 people have been rescued so far from buildings that have at least partially collapsed, the Hualien fire department said.
Some were seen crawling to safety, according to local media reports.
“We know there are people who are trapped inside – we can see lights inside the hotel,” an eyewitness told the BBC.
“People with phones are shining their cellphone lights to let people know they’re there.”
The army has been called in to help emergency workers.
Highways and bridges into the area have been damaged and are closed to traffic. A number of aftershocks hit the area, but there was no word of any tsunami warning.
Hualien is a popular tourist destination on Taiwan’s eastern coast and home to about 100,000 people.
“The president has asked the Cabinet and related ministries to immediately launch the ‘disaster mechanism’ and to work at the fastest rate on disaster relief work,” President Tsai Ing-wen’s office said in a statement.
Lai said the government was urgently repairing a major highway damaged by the quake.
Among the buildings toppled in the quake was the Marshal Hotel in Hualien, where three people were trapped, the Government said.
Four other buildings, including two hotels and a military hospital, also tilted during the quake in Hualien, which is located about 120 kilometres south of the capital, Taipei.
The government said two bridges in the city were either cracked or could not be used due to the quake.
A magnitude 6.1 earthquake struck nearby on Sunday.
Dozens of smaller tremors have been felt throughout the island over several days. Taiwan sits near a junction of two tectonic plates and is regularly hit by earthquakes.
The earthquake happened on the second anniversary of a 6.4-magnitude tremor that killed 117 people in 2016.
Some people in Taiwan are still scarred by a 1999 magnitude-7.6 earthquake in which more than 2000 people died.
Taiwan, a self-ruled island that China considers part of its territory, is prone to earthquakes.
- PNC sources