Taiwan is prone to earthquakes and has felt a few in recent days, including magnitude 5.3 and 6.1 quakes on Sunday.
Four other buildings, including two hotels and a military hospital, also tilted during the quake in Hualien, which is located about 120 kilometres (75 miles) south of the capital, Taipei.
Taiwan's official Central News Agency reported that the ground floor of the Marshal Hotel, a building in Hualien district, had caved in and up to 30 people were believed to be trapped inside.
"It's the biggest quake I've experienced in Hualien in more than 10 years", resident Blue Hsu told Agence France-Presse, who said his home shook violently.
Chen Minghui, a maintenance worker who was rescued after being trapped in the hotel's basement, said the force of the natural disaster was unusual.More news: Colts hire Patriots OC McDaniels as head coach
The quake caused widespread damage in Hualien, a city of 100,000 people.
Scenes of widespread structural damage in the streets have been shown on numerous Facebook live videos filmed by locals. No one was killed in those quakes.
Lewis said she lives on the 12th floor of an apartment complex.