Köhn graduated from the University of Oslo with a cand.theol. degree. Köhn worked as an assistant professor in Biblical Theology at the University of Oslo from 1976 to 1988, and principal of the Practical-Theological Seminary from 1989 to 1993. She was bishop of Hamar from 1993 to 2006 as the first female bishop to be appointed in the Church of Norway. She stepped down from office on 1 November 2006 and was succeeded by Solveig Fiske.