 Moltesen was born in Råhede in Hviding Parish, to farmer Peter Moltesen and his wife Bodil, née Lauritzen.Hviding was located on the northern extremity of Northern Schleswig, a region Denmark had surrendered to Prussia the year before his birth, and consequently his father purchased a second farm in Brørup north of the new border, to ensure that his children could attend a Danish school.Educated in theology at the University of Copenhagen, he made large contributions as a church historian, and supported the thoughts of N. F. S. Grundtvig.