He studied at the University of Berlin, where he obtained his doctorate in 1864, after a brief period in the judiciary. He was appointed associate professor at Marburg in 1870 and, having become a full professor in 1871, moved the following year to Innsbruck, in 1874 to Königsberg, and finally in 1888 to Bonn.
A keen investigator of Roman legal sources, from 1864 he was called by Mommsen to participate in the edition of the Corpus iuris civilis. His editorial work includes the Institutiones (Berlin 1867), the Codex Iustinianus (ibid. 1873-77; 10th ed. ibid. 1929), as well as the Fragmenta de iure fisci, the Epitome Ulpiani (whose collation of the Vatican codex he supervised), the Consultatio veteris cuiusdam iurisconsulti and the Sententiae Pauli, which constitute his contribution to the edition of the Collectio librorum iuris anteustiniani (ibid. 1878-99), carried out in collaboration with Th. Mommsen and W. Studemund. Krüger is also responsible for the revision of Mommsen’s edition of vol. I of the Corpus iuris civilis (Institutiones and Digesta, 15th ed., ibid. 1928) and an edition of the first eight books of the Codex Theodosianus (ibid. 1923-26).
Among his other works are Prozessuale Konsumption und Rechtskraft des Erkenntnisses (Leipzig 1864), Kritik des Just. Codex (Berlin 1867), and Kritische Versuche im Gebiete des römischen Rechts (Marburg 1872), as well as the fundamental Geschichte der Quellen und Literatur des römischen Rechts (Leipzig 1888; 2nd ed. ibid. 1912).