His father, Mads Jensen, oversaw a farm near Holstebro and worked as a sognefoged: an appointed aid to the rural chief of police.

During his childhood, Madsen was taught by a neighboring priest until attending a secondary school in Viborg from 1858 until 1862.

He had intended to continue his travels to England, but was called back to the University of Copenhagen to fill the professorial vacancy left by Henrik Nicolai Clausen in 1874.

[2][3] In 1879, Madsen received his doctorate in theology with the completion of his dissertation on Christian spiritual priesthood: De kristnes aandelige Præstedømme.

From 1879 to 1881, he was involved in the preparation of a new series of pericopes and later, when the church council was established, his fellow theological faculty elected him as their representative from 1884 until 1886.