Taiwan television stations showed footage of some collapsed buildings in the eastern county of Hualien, near the quake's epicentre, and media reported some people were trapped.
The quake hit at 07:58 a.m. (2358 GMT) at a depth of 15.5km (9.6 miles) just off the eastern coast of Taiwan, according to Taiwan's Central Weather Administration. It was the strongest quake to hit the island in 25 years, state media said.
Japan issued an evacuation advisory for the coastal areas of the southern prefecture of Okinawa. Tsunami waves of up to 3 metres (10 feet) were expected to reach large areas of Japan's southwestern coast, according to the Japan Meteorological Agency, which put the quake magnitude at 7.5.
A 30 cm (1 foot) tsunami reached Yonaguni Island at 9:18 a.m. (0018 GMT), JMA said.
The Philippines Seismology Agency also issued a warning for residents in coastal areas of several provinces, urging them to evacuate to higher ground.
The quake was felt in Shanghai, a Reuters witness said. Chinese state media said it was also felt in Fuzhou, Xiamen, Quanzhou and Ningde in China's Fujian province.
The Taipei city government has not received any reports of damage and the city's MRT was up and running soon after.
Taiwan's high speed rail operator said no damage or injuries were reported on its trains, but noted trains will be delayed while it carries out inspections.
Southern Taiwan Science Park, where semiconductor giant Taiwan Semiconductor Manufacturing Co 2330.TW has a plant, said companies were operating without impact.
Taiwan's official central news agency said the quake was the biggest to hit the island since 1999 when a 7.6 magnitude tremor killed around 2,400 people and destroyed or damaged 50,000 buildings in one of Taiwan's worst-recorded quakes.
Japanese public broadcaster NHK said the earthquake registered an intensity of an "Upper 6" in Taiwan's Hualien on Japan's 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.
