He was born at Merseburg in Saxony-Anhalt, then part of Prussia. 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 Romer (2nd ed., 1885) is an excellent treatise on a limited subject (Eng. trans. by SB Platner, Boston, Mass., 1892).

His other chief publications were:

• C. Lucili saturarum reliquiae (1872), including the fragments of Accius and Suetus
• Leben und Werke des Galus Lucilius (1876; suppt. Luciliana, 1884)
• text of Horace (1869; 3rd ed., 1897)
• Quintus Horatius Flaccus, eine litterarhistorische Biographie (1880)
• Quintus Ennius (1884), an introduction to the study of Roman poetry
• Q. Enni carminum religuiae (1884)
• Livi Andronici et Gn. Naevi fabularum reliquiae (1885)
• Der saturnische Vers und seine Denkmäler (1885)
• Noni Marcelli compendiata doctrina (1888)
• De Pacuvii fabulis (1889)
• De Aceli fabulis disputatio (1890).