The natural disaster struck just before midnight local time (1550 GMT) around 21km northeast of the port city Hualien, according to the US Geological Survey.
There was no immediate confirmation of deaths or injuries.
The USGS reported the quake struck about 11.50pm last night local time (4.50am NZT) at a depth of about 9.4km.
There were also no reports of damage at that time.
The government sent residents of the Asian island an alert before it struck, witnesses said.
The latest quake comes just two days after twin tremors struck the island nation within two hours of each other. "The pattern continued with ten more earthquakes on Monday, the largest of which being a magnitude 5.0 quake". Massive cracks have appeared on paved roads in the area and power has been cut to a large number of households.
The "Ring of Fire" is located within the basin of the Pacific Ocean, lined with around 75 percent of the world's total active volcanoes.