In 1837 he went to Munich, and then next year took the prescribed theological examinations at Gießen, after which he entered the ecclesiastical seminary at Mainz, where he was ordained to the priesthood on 19 December 1839.
Moufang's first appointment was as curate in Seligenstadt, where his uncle, Adam Franz Lennig, later vicar-general and dean of the Mainz Cathedral, was pastor.
In November 1868 he was summoned to Rome for the preparatory work of the First Vatican Council, and was assigned to the committee for ecclesiastico-political matters under Karl-August von Reisach.
However, the Hessian grand ducal government refused to confirm his election, so Moufang served as administrator only.
The ten years that he carried this charge while the seminary was shuttered were difficult for Moufang, primarily due to the hostile attitude of the government.
In 1871 he entered the German Reichstag, where he was held in esteem by the Centre Party for his political services and as an intermediary in harmonizing the differences between North and South Germany.
The most prominent feature of Moufang's literary activity was his work in reorganizing and publishing the "Katholik", which in collaboration with Johann Baptist Heinrich he edited from 1851 until his death.
He also paraphrased the Latin Easter hymn O filii et filiae into German as "Ihr Christen, singet hocherfreut" in 1865.