Mølby was formerly part of the German Empire. In the German Empire, the place was called Mölby.
The place is now called Mølby and belongs to Denmark.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Mölby | German Empire | Hadersleben | before the Versailles Treaty |
| Mølby | Denmark | Haderslev | after the Versailles Treaty |
| Mølby | Denmark | Sønderjylland | 1993 |