The U.S. Geological Survey said the quake was centered 13 miles north-northeast of Hualien, a city of more than 100,000 on Taiwan's east coast.
The Central Weather Bureau, which tracks seismic activity in Taiwan, reported the epicenter of the quake was at sea about 18.3 kilometers (11 miles) north of Hualien City.
A hotel and a residential block were the worst hit by the quake in the port city of Hualien, according to the national fire agency.
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Describing the scene at the Marshal Hotel, Hsu said the bottom storeys had been crushed.
Casualties are as yet unknown as rescue services on the scene attempt to use cranes and heavy lifting equipment to reach people possibly trapped in the buildings.
Five more buildings including a hospital had also been damaged, the agency added, with televison footage showing roads strewn with rubble, cracks along highways and damaged buildings tilted at angles. The quakes continue to jolt the area near Hualien County through early Wednesday morning.
Tuesday night's quake follows one over the weekend off the coast of Hualien on the east of Taiwan, which lies along the famed "Pacific Rim of Fire" known for seismic activity from Alaska to Southeast Asia.
Another 5.1 magnitude tremor was felt shortly after. "No injuries were reported at the time of publication", the Taiwan News reported.