Landau studied medicine at the Universities of Breslau, Würzburg and Berlin, obtaining his doctorate at the latter institution in 1870.
After serving as an assistant surgeon during the Franco-Prussian War, he was a lecturer in gynecology at the University of Breslau (1872–76).
In 1892 with his brother, Theodor Landau (1861–1932), he opened a Frauenklinik (Women's clinic) in Berlin that became well known throughout Germany.
From here, he conducted medical research, publishing noted works on myoma and radical vaginal operations.
With his brother, he was co-author of Die Vaginale Radicaloperation: Technik und Geschichte (1896), being later translated into English and published as The history and technique of the vaginal radical operation (1897).