Korsch was born in Tostedt, near Hamburg, to the family of a middle-ranking bank official.
He attended universities at Munich, Berlin, Geneva and Jena, studying law, economics and philosophy. He acquired a Doctorate at Jena in 1910. From 1917 to 1933 he was active in left wing politics in Germany, leaving on the night of the Reichstag fire. After a brief stay in England and Denmark, he and his wife settled in the USA in 1936, teaching at Tulane University, New Orleans, and working at the International Institute for Social Research, New York.
He died in Belmont, Massachusetts in 1961.