Cornelius was born in Lichtenburg, South Africa, and grew up in rural South Africa as one of nine children. Her father and grandfather both fought in the Anglo Boer War and her mother was held in a concentration camp during the war. She and her older sister, Hester Cornelius, moved to Johannesburg in the 1920s, where Johanna eventually started working in a garment factory. Cornelius worked as a machinist in the factory.