Taiwan's Central Weather Administration (CWA) said a 7.2 magnitude earthquake struck near the island on Wednesday morning.
It said the quake hit at a depth of 15.5 kilometers (9.6 miles) with the epicentre around 25 kilometers southeast of the city of Hualien.
Taiwanese broadcaster TVBS posted footage of a collapsed building.
AFP news agency cited a fire department official from Hualien in reports that buildings had collapsed.
"Two buildings have collapsed and some people are believed to be trapped. We don't have more information at the moment," AFP quoted the official as saying.
Quake 'the strongest in 25 years' — Taipei Seismology Centre
The director of Taipei's Seismology Centre, Wu Chien-fu, told reporters that the earthquake was "the strongest in 25 years."
"The earthquake is close to land and it's shallow. It's felt all over Taiwan and offshore islands... it's the strongest in 25 years since the (1999) earthquake," Wu told reporters, referring to a September 1999 quake measuring 7.6-magnitude that killed 2,400 people.
"The public should pay attention to relevant warnings and messages and be prepared for earthquake evacuation," Wu warned.
Taiwan experiences regular seismic activity as the island is situated close to the junction of two tectonic plates, while nearby Japan experiences around 1,500 jolts every year.
Japan downgrades tsunami warning to 'advisory'
The Japan Meteorological Agency (JMA) downgraded an earlier tsunami warning for Japan's southern islands to a "tsunami advisory."
The JMA said waves as high as 1 metre (3.3 feet) could be recorded in the region.
At 9.18 am local time, the JMA reported that a 30 cm tsunami had reached Yonaguni Island.
Japanese authorities issued an evacuation advisory for coastal areas near the southern prefecture of Okinawa.
"Evacuate!" said a banner on Japanese national broadcaster NHK.
"Tsunami is coming. Please evacuate immediately," an anchor on NHK said. "Do not stop. Do not go back."
Japan's Self Defense Force dispatched aircraft to gather information about the possible impact tsunami waves could have around the Okinawa region and were preparing shelters for evacuees if necessary.
AFP news agency reported that flights at the Naha Airport in Okinawa had been suspended as a precautionary measure, citing a transport ministry official.
In March, 2011, a 9.0 magnitude earthquake struck the main Japanese island of Honshu. It triggered a tsunami which disabled the power supply that cooled three reactors at Japan's Fukushima nuclear power plant, triggering a nuclear disaster. Around 18,500 people were killed or were missing.
Philippines warns of 'high tsunami waves'
The Philippines also issued warnings of "high tsunami waves" and called for the evacuation of coastal areas.
"The people in the coastal areas of the following provinces are strongly advised to immediately evacuate to higher grounds or move farther inland," the state seismology institute said in an advisory for 23 provinces where it said "high tsunami waves" were expected to hit.
The first tsunami waves were expected to arrive between 00:33 and 02:33 UTC which "may not be the largest and these waves may continue for hours."
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