Born in Reudnitz near Leipzig, Penck became a university professor in Vienna from 1885 to 1906, and in Berlin from 1906 to 1927. There he was also the director of the "Institute and Museum for Oceanography" by 1918. He dedicated himself to geomorphology and climatology and raised the international profile of the "Vienna School of physical geography".
With Eduard Bruckner, he was co-author of Die Alpen im Eiszeitalter, a work in which the two scientists identified the four ice ages of the European Pleistocene (Gunz, Mindel, Riss, Würm). These being named after the river valleys that were the first indication of each glaciation. In 1945, Penck died in Prague.
In memory of Penck, the painter and sculptor Ralf Winkler adopted the nom de plume A. R. Penck in 1966. The glacier of Penckbreen in Wedel Jarlsberg Land at Spitsbergen, Svalbard is named after him.