Karl Alexander von Müller was the eldest son of Marie von Burchtorff and the then Munich police chief and later Bavarian Minister of Culture, Ludwig August Müller. He studied law and history in Munich and Oxford, received his doctorate from the Ludwig Maximilian University of Munich (LMU) in 1908, and completed his habilitation (postdoctoral lecturing qualification) there in 1917. Together with Paul N. Cossmann, he was editor of the increasingly nationalistically oriented Süddeutsche Monatshefte (‘South German Monthly‘) from 1914 onward. Honorary professor until 1928, he subsequently took over the chair for Bavarian regional history and, from 1936 onward, the chair for medieval and modern history at the LMU. From 1935 until 1944 he was editor of the Historische Zeitschrift and from 1928 until 1945 secretary of the Historical Commission at the Bavarian Academy of Sciences and Humanities, being appointed president there—albeit without nomination from the Academy itself—by Reich Minister of Education Bernhard Rust in March 1936. He held this office until the end of 1943. At the request of his student Walter Frank, he nominally headed up the ‘Research Department Jewish Question‘ at the ‘Reich Institute for the History of the New Germany‘ from 1936 onward too.
Due to all these positions in academia and historical studies, his national-conservative attitude, his inspiring teaching activities, and his engaging manner, von Müller—who had been a member of the Nazi Party since 1933—was one of the most influential German historians of that time and an important exponent of a historiography that yielded uncritically to the spirit of the Nazi regime. Hence it is hardly surprising that a majority of his students—in excess of 200 of whom had their doctorates supervised by him—were loyal to the regime.
Removed from office in 1945, he retired three years later and was granted the legal status of professor emeritus in 1956. A member of the Academy of Fine Arts in Munich from 1953 onward, he was awarded the Bavarian Order of Merit in 1959.