Wednesday morning’s quake was magnitude 7.2 on the Richter scale, while the US Geological Survey put it at 7.4 and Japan’s meteorological agency put it at 7.7.
The earthquake led to a small tsunami in some coastal areas of Japan, but warnings were later lifted.
Four people have died and at least 57 have been injured in eastern Taiwan’s Hualien County – the epicentre of the quake – which struck during morning rush hour at 7.58am local time (3am UK time).
Its epicentre was around 11 miles southwest of Hualien and about 22 miles deep.
In the capital Taipei, in the north of the island, tiles fell from the roofs of older buildings and within some newer office complexes.
Meanwhile, more than 87,000 households in Taiwan were without power, according to the island’s electricity supplier.
Train services across Taiwan – which is home to 23 million people – were suspended, as was the metro.
A five-storey building in Hualien was heavily damaged. The first floor collapsed, leaving the rest leaning at a 45-degree angle.
Traffic along the east coast was brought to a virtual standstill, with landslides and falling debris hitting tunnels and highways in the mountainous region.
The national legislature in Taipei, a converted school built before the Second World War, also had damage to walls and ceilings.
Schools evacuated their students to sports fields, equipping them with yellow safety helmets.
Some also covered themselves with textbooks to guard against falling objects as aftershocks continued.
Taipei resident Hsien-hsuen Keng said: “Earthquakes are a common occurrence, and I’ve grown accustomed to them. But today was the first time I was scared to tears by an earthquake. I was awakened by the earthquake. I had never felt such intense shaking before.”
She said her fifth-floor apartment shook so hard that “apart from earthquake drills in elementary school, this was the first time I had experienced such a situation”.
Japanese Prime Minister Fumio Kishida has said his country stands ready to support Taiwan following the quake.
Japan’s meteorological agency described the earthquake as very shallow, which can cause greater damage.
The agency also said people “must be vigilant” for aftershocks, which could be of similar intensity for about a week.
Japan’s chief cabinet secretary Yoshimasa Hayashi said there has been no report of injury or damage in Japan.
He urged residents in the Okinawa region to stay on high ground until all tsunami advisories were lifted.
The Philippines Seismology Agency also issued urged residents in coastal areas of several provinces to evacuate to higher ground.
Chinese media confirmed the earthquake was felt in Shanghai and several provinces along China’s south-eastern coast.
China and Taiwan are about 100 miles apart. China issued no tsunami warnings for the Chinese mainland
Multiple aftershocks were felt in Taipei in the hour after the initial quake. The US Geological Society said one of the subsequent tremors was seven miles deep and had a magnitude of 6.5.
Taiwan lies along the Pacific Ring of Fire, a line of seismic faults where most of the world’s earthquakes occur.
Taiwan’s worst quake in recent years struck in 1999, with a magnitude of 7.7, causing 2,400 deaths, injuring around 100,000 and destroying thousands of buildings.
In March 2011, a 9 magnitude earthquake was the strongest in Japan’s history – triggering a massive tsunami and the world’s worst nuclear crisis since Chernobyl.
