Premier William Lai said two people had died in the quake in the port city of Hualien and 114 were injured, some seriously. He gave no further details.
The national fire agency said at least four buildings had fallen or been damaged, with televison footage showing roads strewn with rubble and cracks in highways.
Images showed the collapsed Marshal Hotel slanted on its side, partially crumpled into the ground, as rescuers tried to pull people to safety.
Taiwan's president Tsai Ing-wen said rescuers from around the island were preparing to help.
Also Read
"We will get into disaster relief work at the fastest speed," she said in a post on her Facebook page.
One Facebook livestream showed rescuers at the foot of the darkened Marshal Hotel building and a crane carrying them up to the higher floors, which were leaning at an angle.
Officials from Hualien fire department said 28 people had been rescued from the hotel and a residential building.
One Facebook user in Hualien told of damage around him.
"The quake is so big... There are cracks on the wall, even the fridge moved," he said.
The quake hit at 23:50 pm (local time) around 21 kilometres (13 miles) northeast of Hualien, according to the United States Geological Survey.
It follows almost 100 smaller tremors to have hit the area in the last three days and comes exactly two years since a quake of the same magnitude struck the southern Taiwanese city of Tainan, killing more than 100 people.
It was the only high-rise in Tainan to crumble completely in the quake, which came two days before Lunar New Year, when many people would have been visiting relatives for the biggest celebration of the Chinese calendar.
The safety of the building was called into question immediately after the disaster, when metal cans and foam were found to have been used as fillers in the concrete and residents said there had been cracks in the structure.
Taiwan lies near the junction of two tectonic plates and is regularly hit by earthquakes.
The island's worst tremor in recent decades was a 7.6 magnitude quake in September 1999 that killed around 2,400 people.
Disclaimer: No Business Standard Journalist was involved in creation of this content