The natural disaster was felt across Taiwan, and some buildings and roads in Hualien, in eastern Taiwan, were damaged.
Hualien is one of Taiwan's most popular tourist hubs as it lies on the picturesque east coast rail line and is near to popular Taroko Gorge.
The injured are mainly from the Marshal Hotel, and a few of the injured were in the city buildings.
Kiwi Emily Clarke and two of her friends were staying near a beach just out of Hualien when the quake struck.More news: No tsunami on East Coast
Chen Minghui, a maintenance worker who was rescued after being trapped in the hotel's basement, said the force of the quake was unusual.
The Taiwan government said emergency workers were trying to free people who are trapped in the Marshal Hotel, which partially collapsed. Most are minor and cause little or no damage.
Clarke said everyone in the hostel is out and there have been a couple of aftershocks.
The government said two bridges in the city were either cracked or could not be used due to the quake. We dare not go back home now.More news: Father Who Attacked Larry Nassar Speaks Out About The Incident
"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", the Taiwan president's office said in a statement.
The quake's centre was about 20 kilometres east-northeast of Hualien, according the U.S. Geological Survey.
Meanwhile, media reports said that a hotel has collapsed after the quake hit Taiwan's east coast on Tuesday.
A magnitude-7.6 quake in central Taiwan killed more than 2,300 people in 1999.More news: Powell sworn in as Fed chairman
- Deputy Killed In Colorado Springs Shooting
- In Chicago, Kashmiris Assured Of Pakistan's Support Until Freedom From India
- Man arrested, charged with circulating child pornography on social media
- Man United legend tips Mkhitaryan to thrive at Arsenal
- Lallana sent off for grabbing opponent's throat in Under-23 outing
- Ex-Patriot Brandon Browner calls out Bill Belichick over Malcolm Butler benching
- HTC U12 Apparently Shown Off During 5G Industry Event
- Ben Platt to star in new Netflix series from Ryan Murphy
- Winter weather could make for slick afternoon commute
- The Cloverfield Paradox Is Now Streaming on Netflix