Balfour Brickner was born on November 18, 1926, in Cleveland, Ohio, United States. He was the son of Barnett and Rebecca Brickner. His father was himself a prominent figure in Reform Judaism and served for many years as the rabbi of Cleveland's Congregation Anshe Chesed (then known as the Euclid Avenue Temple). Rebecca Brickner (1894-1988) was a close associate of Henrietta Szold, and, like her husband, an active Zionist, as well as a leading Jewish educator. He had a sister, Joy Rabinowitz.