The quake struck at 7:51 am local time centred 62 kilometres east of Hualien city at a depth of 20 kilometres, with tremors felt in the capital Taipei for a few seconds.
A 5.9 magnitude quake hit the same area on June 8, with no casualties.
But a strong 6.2 magnitude quake that struck the island on June 3 left two dead and 21 injured, and was also felt in Hong Kong, more than 700 kilometres away.