Born in Hamburg, Germany, Muller was a child when his family fled Nazi Germany. He spent his teenage years in Los Angeles, even acting in several Hollywood movies before enrolling at the University of California, Los Angeles, from which he graduated in 1948. He earned a degree in politics from Oxford University, where he was a Rhodes Scholar, and received a doctorate from Cornell University. Before his tenure at Hopkins, Muller served as a vice president of public affairs at Cornell and as director of its Center for International Studies.
After his retirement. Muller remained active in the Hopkins community and was awarded an honorary doctorate of humane letters in 2000.