Frank Putnam was born in New Britain, Connecticut, on August 3, 1917, to Austrian-born Franz and Henrietta Holzmann Poglitsch. His parents died of tuberculosis before he was three years old and he grew up in the New Britain Children's Home. Putnam was an excellent student in high school and was encouraged by a local bank manager, L. Marsden Hubbard. He changed his name around the time he left for Weslayan University in Middleton, Connecticut. He earned a BA in chemistry in 1939 and then an MA in 1940. He earned a Ph.D. from the University of Minnesota in 1942 and took a postdoctoral position at Duke University.

The Putnams left for Florida in 1955 to help found the University of Florida College of Medicine's biochemistry department. They stayed for ten years before moving on to Indiana University in Bloomington, to its new Division of Biological Sciences. In the 1970s and 1980s he made ten trips to Hiroshima and Nagasaki on behalf of ABCC/RERF.