Bärnighausen studied Chemistry at Leipzig University and received his diploma after a diploma thesis with Leopold Wolf in 1955. In May 1958, he flew from East Germany to University of Freiburg, where he worked with Georg Brauer. He finished his doctorate in the group of Georg Brauer in 1959. In 1967, he received his habilitation. From 1967 to 1998, he was a professor for inorganic chemistry at the University of Karlsruhe.