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After World War I, Muhs studied law in Göttingen and graduated in 1922. He opened a law office and became a member of the NSDAP in 1929. From 1930, he was a member of the Prussian State Parliament, and after 1933 he became the district president of Hildesheim.
In 1935, Muhs was the Secretary of State in the Reichsministerium für Kirchenfragen. His synchronization efforts and theological incompetence caused many disputes with the churches.
Against the orders of Heinrich Himmler, who wanted to draw distance between the Schutzstaffel and the Church, Muhs participated in the funeral of Archbishop Karl Joseph Schulte in an SS uniform in 1941. Muhs, who had the rank of an SS-Oberführer, was expelled from the SS. Nevertheless, after the death of Hans Kerrl, he succeeded Kerrl as Minister for Church Affairs until 1945.