After World War I, the family moved to Johannesburg, where he was educated at Parktown Boys' High School and the University of the Witwatersrand.
His academic positions included visiting professorships at Oxford, Harvard, Pennsylvania, Ann Arbor, UCLA, New York, Hebrew University of Jerusalem, Hiroshima, Tokyo, and the Taiwan Army Medical Centre.
Penn originated innovative techniques in plastic surgery, notably the Brenthurst Splint, which was standard for many years for jaw fractures.
He helped to initiate plastic and reconstructive surgery in other countries, including Israel (during the 1948 war), Zimbabwe (then Rhodesia), Kenya, Gabon (then French Equatorial Africa, at the invitation of Albert Schweitzer at Lambaréné), Japan (assisting Hiroshima and Nagasaki victims) and Taiwan.
Jack Penn wrote a number of books, mainly of a philosophical nature, which include his Letters to my Son (1975) – letters that were addressed to his son John who, like himself, became a plastic and reconstructive surgeon and served as president of the American Society for Aesthetic Plastic Surgery; The Right to Look Human: an autobiography (1974); Reflections on Life (1980); and To think is to live (nd).