Setting RadDropDownButtonElement MinSize property does not make the RadDropDownButton control stretch to fit its element.
Currently, the issue can be avoided through adding the following three lines of code:
this.radDropDownButton1.RootElement.StretchHorizontally = false;
this.radDropDownButton1.RootElement.StretchVertically = false;
this.radDropDownButton1.RootElement.SaveCurrentStretchModeAsDefault();