The quake, which knocked out power in several parts of the capital Taipei, hit at 7.58am on Wednesday (local time) at a depth of 15.5km just off the eastern coast of Taiwan, according to Taiwan's Central Weather Administration.
Seven people have died, at least 700 are injured and 77 are trapped in tunnels and collapsed buildings, authorities said.
Taiwan television stations showed footage of buildings at precarious angles in Hualien, where the quake struck as people were going to work and school. At least 26 buildings have collapsed, more than half in Hualien.
"It was very strong. It felt as if the house was going to topple," said 60-year-old Taipei hospital worker Chang Yu-Lin.
Video showed rescuers using ladders to help trapped people out of windows, while elsewhere there were massive landslides, as strong tremors in Taipei forced the subway system to close briefly, although most lines resumed service.
Fire authorities said about 60 of the roughly 77 trapped were caught in a tunnel just north of Hualien city, with two Germans among those trapped in another tunnel. The government put the number of injured at 736.
"At present the most important thing, the top priority, is to rescue people," said President-elect Lai Ching-te, speaking outside one of the collapsed buildings in Hualien.
The rail link to the area was expected to re-open on Thursday, Lai, who is set to take office next month, told reporters.
Taiwan's air force said six F-16 fighter jets had been slightly damaged at a major base in the city from which jets are often scrambled to see off incursions by China's air force, but it expected the aircraft to return to service very soon.
The Philippines Seismology Agency also issued a warning for residents in coastal areas of several provinces, urging them to evacuate to higher ground.
Taiwan also issued a tsunami warning, but reported no damage from that, and the Pacific Tsunami Warning Center in Hawaii later said the risk of damaging tsunami waves had now largely passed.
Aftershocks could still be felt in Taipei, with more than 50 recorded, weather officials said.
Chinese state media said the quake was felt in China's Fujian province, while a Reuters witness said it was also felt in Shanghai.
The Taipei city government said it had not received any reports of major damage and the city's metro, the MRT, was up and running soon after the tremor, while electricity operator Taipower said more than 87,000 households in Taiwan were still without power.
Southern Taiwan Science Park, where semiconductor giant Taiwan Semiconductor Manufacturing has a plant, said companies were operating without impact. TSMC said its safety systems are operating normally.
Taiwan's Central Weather Administration said the quake registered the second-highest intensity of an "Upper 6" in Hualien county, on the 1-7 intensity scale.
In an Upper 6 earthquake, most unreinforced concrete-block walls collapse and people find it impossible to remain standing or move without crawling, the Japan Meteorological Agency says.
