The 6.4-magnitude quake struck just before 04:00AM local time when most people were at home asleep.
A baby was among at least four people killed when a high-rise building, containing 100 homes, collapsed.
At least 30 people remain missing. Tainan’s mayor said people were alive but trapped under the rubble and all means would be used to rescue them.
Taiwan President Ma Ying-jeou, who toured the city of two million, said shelters would be set up for those who had lost their homes.
Television footages showed rescue workers frantically trying to reach people trapped in collapsed buildings, using ladders to climb over piles of rubble.
One of the worst affected was the 17-storey Wei Kuan apartment complex, home to at least 256 people.
More than 200 people were rescued, but a baby, young girl and two adult men did not survive, officials said. At least 70 people were taken to hospital.
Interior Minister Chen Wei-jen said he feared more people may have been in the fallen apartment block than usual as families gathered to celebrate Chinese New Year.
Chen Wei-jen said investigators would examine whether the building’s construction met requirements.
Residents told how they were able to escape from their homes in the block, using their own tools and ladders.
The earthquake was shallow, meaning its effects would have been amplified, the US Geological Survey (USGS) said.
There have also been at least five aftershocks. The quake was felt in the capital Taipei, 200 miles away.
Although the damage does not appear to be widespread, a number of tall buildings have been left leaning precariously.
There are also reports of power outages, and transport links have been disrupted on what is one of the busiest travelling days of the year ahead of the Chinese New Year holiday.
Taiwan lies near the junction of two tectonic plates and often sees tremors.
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