A report from the US Geological Survey confirms Taiwan recorded a 6.4 magnitude and 9.4km deep earthquake around 22km north-northeast of Hua-lien.
The earthquake struck at 11:50pm local time.
Officials said two hotel employees were killed while about 144 other people sustained injuries.
“Two people were unfortunately killed, and 114 have suffered light or severe injuries,” Taiwan’s Premier William Lai told an emergency government meeting.
Taiwanese media reported that a separate hotel known as the Beautiful Life Hotel was tilting.
The Central News Agency reported that the ground floor of the Marshal Hotel, a building in Hualien district, had caved in and people were believed to be trapped inside.
An official from the Ministry of Interior’s fire station division said people were trapped in the buildings in Hualien.
“The president [Tsai Ing-wen] has asked the cabinet and related ministries to immediately launch the ‘disaster mechanism’ and to work at the fastest rate on disaster relief work,” the president’s office said in a statement.
BBC Taipei correspondent Cindy Sui said the hotel which had collapsed on its columns and is tipped over at about 45 degrees was the 300-room Marshal Hotel.
“What we’re hearing right now is that in the city of Hua-lien in eastern Taiwan several buildings have collapsed or are near collapsing. One of them is a hotel, called the Marshall Hotel.”
She continued, “We have heard from the defence ministry spokesman that they have sent … 88 soldiers, to assist the fire department out there and the local media are reporting that there might be many people trapped in this hotel.
“We’re also hearing that there might be a hot pot restaurant that has also collapsed.
“The military said that the reports that a military hospital had collapsed, they’re said they had yet to confirm, that they had not heard that.”
“From the images shown on TV, it looks like the hotel hasn’t collapsed yet but its tilted very, very severely on one side towards the street and some of the lower floors seem to be crushed.
“We’re seeing images on TV that the’re trying to get into some of the upper floors with ladders and there also are soldiers assisting them.
“About 250 soldiers are on standby to assist.”
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Mr Lai said the government was urgently repairing a major highway damaged by the quake.
The government said two bridges in the city were either cracked or could not be used due to the quake.
There have also been several aftershocks above magnitude 5, and an earlier quake of magnitude 6.1 struck nearby on Sunday.
Search teams from other areas were headed to Hualien.