Police said the man, identified as Jaryanto, 36, and his girlfriend, identified as Sopiah, 40, originally left their documented places of official employment in 2012 and have since made a living doing odd jobs in the Lishan area of Taichung.
On Monday night the couple apparently decided to surrender to the immigration authorities in the hope of being repatriated to Indonesia, CNA reported.
However, as it was already night they spent the evening in a grocery store owned by an Indonesian national, who allowed them to stay there after he closed the store and went home.
A neighbor reported that he heard the couple arguing at about 2 a.m. on Tuesday, but was unable to understand what they were fighting about.
Police alleged that Jaryanto violently beat his girlfriend and on discovering that she was not breathing placed her in a cardboard box with the intention of disposing of the body.
When the store owner returned on Tuesday morning, he found Jaryanto sobbing and Sopiahs lifeless body in the box. She was rushed to a local hospital, but all efforts to revive her failed.
Jaryanto refused to talk to police after he was arrested. The case will now be turned over to the Yilan District Prosecutors Office.