Nielsen was born in Durup, Salling, on 8 April 1941.[1] She obtained a teaching degree in 1964 and worked as a teacher until 1973.[2] She was appointed minister of education to the cabinet of Prime Minister Poul Hartling on 19 December 1973.[2] She replaced Ritt Bjerregaard in the post.[3] Nielsen was in office until 13 February 1975[2] and was replaced by Ritt Bjerregaard in the post.[4]
Nielsen served in the Danish parliament as part of Venstre for three terms: 1972–1973, 1975–1977 and 1979–1980.[1] She resigned from the parliament in 1980.[4] Then she served in the European Parliament between 1979 and 1994.[2]