Kahn's father was Bernhard Kahn, a son of Michael Kahn and Franziska Baer, a German-Jewish industrialist and banker who participated in the 1848 Revolt, and was condemned to death. He escaped to the United States, was naturalized an American citizen, and then returned to Germany ten years later to court and on October 17, 1860, marry Emma Stephanie Eberstadt, whom he married on the condition that he not return to the United States. The couple had eight children and Otto was the fifth child and third son.