Before and during World War I, he studied at the University of Vienna, graduating in 1916 in history and geography. In 1927 he received his Doctor of Philosophy from the Faculty of Arts with his dissertation on the settlement of the Ljubljana Marshes.
Later he was employed as a secondary school teacher. Between 1938 and 1966, he was a professor of geomorphology at the Department of Geography at the University of Ljubljana, succeeding professor Artur Gavazzi in 1938. With his work in this field he established his well-known geomorphological school.
In 1935–1936, the prestigious publishing house Slovenska matica published his monumental work Geografija Slovenije (The Geography of Slovenia) in two volumes with a general regional part, later extended with four additional books between 1954 and 1960, with a detailed regional description of particular areas of Slovenia: the Alps, Styria with Prekmurje and the Mežica Valley, the Sava Valley, and the Slovenian Littoral.
Between 1947 and 1960, Melik was head of the Department of Geography at the Faculty of Arts. Between 1948 and 1966, he was head of the Geographical Institute of the Slovenian Academy of Sciences and Arts.
Between 1946/1947 and 1949/1950, he was chancellor of the University of Ljubljana, and he served twice as dean of the Faculty of Arts in 1940/1941 and 1945/1946. He retired in 1966. He died in Ljubljana.
In 1976, the Geographical Institute of the Slovenian Academy of Sciences and Arts, founded in 1946, was renamed the Anton Melik Geographical Institute in his honor.
Slovenian Academy of Sciences and Arts.