Born in the town of Hauerz (now Bad Wurzach) in the Allgäu, Leiprecht studied philosophy and theology at the University of Tübingen from 1923 to 1927.
On 24 March 1928 he was ordained a priest by Bishop Johannes Baptista Sproll at Rottenburg Cathedral.
Over the next five years, he served as a vicar at Holy Cross Minster in Schwäbisch Gmünd and at St. George's Church in Stuttgart.
Leiprecht served as the city priest of Rottweil from 1942 to 1947 before becoming vicar capitular at Rottenburg Cathedral.
The next year, Leiprecht was elected the Bishop of Rottenburg on 21 June, Pius XII officially named him to the post on 4 July and he was enthroned on 8 September.