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He studied classical philology at the Universities of Göttingen and Bonn. At Bonn he was a pupil of Hermann Usener and Franz Bücheler. In 1872–74 he was a member of the German Archaeological Institute in Rome, where he became a close associate of Theodor Mommsen and Ulrich von Wilamowitz-Moellendorff. Afterwards, he taught classes in Elberfeld and at the Askanische Oberschule in Berlin.
In 1879 he became an associate professor of classical philology at the University of Breslau, followed by professorships at Rostock (1882), Greifswald (1883) and Strasbourg (1886). In 1897 he returned to Göttingen, where he was elected a full member of the Göttingen Academy of Sciences.
Kaibel published several editions of works from the Second Sophistic era, as well as highly regarded editions of Sophocles' Electra and Antigone. He was editor of the journal "Hermes" (1882 to 1901), and contributed numerous articles on Greek comedy to the first four volumes of Georg Wissowa's Realencyclopädie der Classischen Altertumswissenschaft (1894–1901).
- Epigrammata Graeca ex lapidibus conlecta, (1878)
- Supplementum epigrammatum Graecorum ex lapidibus conlectorum, (1879)
- Dionysios von Halikarnassos, (1885)
- Deipnosophistai of Athenaeus of Naucratis (in Bibliotheca Teubneriana, 1887–90)
- Poetarum Comicorum Graecorum Fragmenta (1890)
- Inscriptiones Italiae et Siciliae (IG XIV, 1890)
- Athenaiôn Politeia of Aristotle (Volume 1 & 2 1891, Volume 3 1898), with Ulrich von Wilamowitz-Moellendorff
- Protreptikos of Galen, (1894)
- Elektra of Sophocles, (1896)
- Antigone of Sophocles, (1897)
- Phrynichos, (1899)
- Cassius Longinus, (1899)
- This article is based on a translation of an equivalent article at the German Wikipedia, its source being listed as NDB/ADB Deutsche Biographie.