Müller was born in Merseburg in the Province of Saxony. After graduating from Humboldt University, Berlin and the University of Halle, he lived for five years in the Netherlands, working on his Geschichte der klassischen Philologie in den Niederlanden (1869). Unable to obtain a university appointment in Germany, he accepted (1870) the professorship of Latin at the Imperial Historico-Philological Institute in St Petersburg.
Müller was a disciple of the methods of Richard Bentley and Karl Lachmann. His De re metrica poetarum latinorum (1861) represents a landmark in the investigation of the metrical system of the Roman poets (the dramatists excepted), and his Metrik der Griechen und Römer (2nd ed., 1885) is an excellent treatise on a limited subject (Eng. trans. by Samuel Ball Platner, Boston, Mass., 1892).
His other chief publications were: