Hensel was born in Groß-Barten near Königsberg, Prussia. He was the son of the landowner and entrepreneur Sebastian Hensel, brother of the mathematician Kurt Hensel, grandson of the composer Fanny Mendelssohn and the painter Wilhelm Hensel. Fanny was the sister of Felix Mendelssohn Bartholdy, daughter of Abraham Mendelssohn Bartholdy, and granddaughter of philosopher Moses Mendelssohn, and entrepreneur Daniel Itzig. Both of Hensel's paternal grandmothers and his mother were from Jewish families that had converted to Christianity.
Hensel became a professor of philosophy at Heidelberg and Erlangen, where he taught until 1928. At Erlangen, Hensel was the supervisor of Hans Reichenbach's PhD dissertation on the theory of probability.