After studying at Königsberg, Bonn and Berlin, Hirschfeld received his doctorate in 1863 in Königsberg. He habilitated in 1869 in Göttingen and in 1872 Professor of History at the University of Prague. In 1876 he moved to the chair of Ancient History, Archaeology and Epigraphy at the University of Vienna, where he founded an Archaeological and Epigraphic seminar with Alexander Conze. In 1885, Hirschfeld successor Theodor Mommsen as a professor of ancient history at the Friedrich- Wilhelms-Universität, now Humboldt University in Berlin, and Director of the Institute of Archaeology. At the same time he was admitted to the Berlin Academy. He became professor emeritus in 1917.
Hirschfeld was mainly active in the field of Latin epigraphy. He published several volumes of the Corpus Inscriptionum Latinarum, especially with the inscriptions of Gaul and the two Germanic provinces. With this geographical area, he was also in his research, in addition to numerous questions of Roman administrative history.
- The Getraideverwaltung [ sic] of the Roman Empire. In: Philologus 29, 1870, pp. 1-96.
- Investigations in the field of Roman administrative history, vol 1: The imperial administration officials to Diocletian, Berlin 1877 [more not published ]; 2 neubearb. Ed Berlin 1905 [ ND Zurich 1975 ].
- Lyon in the Roman period, Vienna 1878.
- Kleine Schriften, Berlin, 1913.