Strassmann was born at Boppard in Germany and educated at the Technical University at Hannover. He taught at Hannover and at the Kaiser Wilhelm Institute before being appointed to the chair of inorganic and nuclear chemistry at the University of Mainz in 1946. In 1953 he became director of chemistry at the Max Planck Institute.

In 1938 Strassmann collaborated with Otto Hahn on the experiment that first clearly revealed the phenomenon of nuclear fission.