Mölders was born on 18 March 1913 in Gelsenkirchen, the son of teacher ("Oberlehrer") Victor Mölders and his wife Annemarie Mölders, née Riedel. He was the third of four children, with an older sister, Annemarie, an older brother, Hans, and a younger brother, Victor. After his father, a Reserve "Leutnant" in the King's 145th Infantry Regiment, was killed in action on 2 March 1915 in the Argonne Forest in France, his mother moved the family into her parents' house in Brandenburg an der Havel.