He was a disciple of historian Theodor Mommsen (1817–1903), who encouraged Wilcken to take a position as cataloguer of papyri following graduation.
Mommsen was also instrumental in Wilcken succeeding Eduard Meyer (1855–1930) as associate professor of ancient history at the University of Breslau in 1889.
Afterwards, he was a professor at the universities of Würzburg (from 1900), Halle (from 1903, where he was again a successor to Eduard Meyer), Leipzig (from 1906) and Bonn (from 1912), where he succeeded Heinrich Nissen (1839–1912).
Later on, he served as a professor at Munich (from 1915) and Berlin (from 1917), where he was successor to Otto Hirschfeld (1843–1922).
Wilcken was a German pioneer of Greco-Roman papyrology, and is credited for amassing an extensive archive of Ptolemaic papyri documents and ostraca.