Kranz studied classical philology at the University of Berlin from 1903 to 1907 with Ulrich von Wilamowitz-Moellendorf, Hermann Diels and Eduard Norden.
In 1932, he joined the University of Halle as an honorary professor of classical languages.
After the takeover by the Nazis, he experienced political difficulties because his wife was Jewish.
In 1937 he lost his full teaching license, and in 1943 he accepted an invitation from the University of Istanbul and taught there until 1950.
From 1950 to 1955 he served as an honorary professor of ancient history at the University of Bonn.