Quentin Burdick was born in Munich, North Dakota, as the oldest of three children of Usher Lloyd Burdick and Emma Cecelia Robertson. His father was a Republican politician who served as Lieutenant Governor of North Dakota (1911–1913) and a U.S. Representative (1935–1959). His mother was the daughter of the first white settler in the area of North Dakota that lies west of Park River. He was the brother of Eugene Allan Burdick, who was judge of the Fifth Judicial District of North Dakota from 1953 to 1978. His sister Rosemary was married to Robert W. Levering, who was a U.S. Representative from Ohio (1959–1961).