No injuries were reported.
The quake's epicenter was at sea, 29 kilometers north northeast of Hualien County Hall, at a depth of 10.4 km.
At 1:25 p.m., a magnitude-4.2 earthquake hit eastern Taiwan, with Yilan's Nan'ao Township registering an intensity of four and Hualien's Heping Township an intensity of three.
The epicenter of that quake was also at sea, northeast of Hualien County Hall, at a depth of 19 km.
The Central Weather Bureau said the two quakes were aftershocks of a magnitude-5.6 quake that struck eastern Taiwan April 27.
Three other earthquakes of magnitude 3.7 or 3.8 struck Hualien in eastern Taiwan between morning and noon Sunday, all of which were also aftershocks of the April 27 quake, according to the bureau.