The quake hit just after midday (0400 GMT) about 30 kilometres (19 miles) off the coast of Hualien County at a shallow depth of six kilometres.
The US Geological Survey reported a lower 5.9-magnitude reading and a depth of 12 kilometres.
There were no immediate reports of damage or casualties.
“The earthquake was felt all over Taiwan because it’s very shallow,” Chen Kuo-chang, head of the weather bureau’s seismological centre, told reporters.
“There have been eight aftershocks so far and we expect more aftershocks in the next three days.”
An AFP reporter in Taipei said the shaking in the capital felt less intense than previous earthquakes this year.
Taiwan’s subway and railway authorities both said trains were running at reduced speed but services had not been halted.
Taiwan is regularly hit by earthquakes as the island lies near the junction of two tectonic plates.
Some earthquakes of 6.0 or more can prove deadly, although much depends on where the quake strikes and at what depth.
A much stronger 6.9-magnitude tremor struck Taiwan’s eastern coast in September, killing one person and bringing down a handful of buildings.