Nørby was born in Copenhagen, Denmark, the daughter of opera singer Einar Nørby. She studied two years at the Danish Royal Theatre. She has received a number of awards and recognitions including the Ingenio et Arti medal in 2006. At the 27th Guldbagge Awards she was nominated for the award for Best Actress for her role in Freud's Leaving Home. She has been married a number of times. First in 1956 to architect Mogens Garth-Grüner, and then to actor Henrik Wiehe. She met her next husband, Italian pop singer/actor Dario Campeotto, on the set of a film they were shooting in 1962. They were married in 1963, and had a son, actor Giacomo Campeotto, in 1964. They were divorced in 1969. She married a fourth time to actor Jørgen Reenberg in April 1970. She is currently married to pianist/composer, Svend Skipper.
What a Pity About Daddy
1968
Hooray for the Blue Hussars
1970
The Kingdom II
1998
Toscana
2022
The Kingdom
1994
Erik Soya's 17
1965
Landsbylægen
1961
Like It Never Was Before
1995
Fra "Harlekin" til "Krøniken": 60 års TV-drama
2011
Smykketyven
1990
A Place Nearby
2000
Vandalism
1977
Crazy Paradise
1962
The Best Intentions
1992
Life with Daddy
1967
De sjove aar
1959
Babette's Feast
1987
Ladies Man
1969
Help! I'm a Fish
2000
Det lille hotel
1958
Kick Me in the Traditions!
1979
Sømand i knibe
1960
The Girl and the Press Photographer
1963
Watch Your Back, Professor!
1977
Louises hus
1977
God, Smell and Her
2009
Everlasting Moments
2008
Jauja
2014
Shake It All About
2001
The Honour of the House
1999
The Inheritance
2003
Going for Broke
1977
Freud Leaving Home
1991
Hamsun
1996
The Musketeers
1961
What No One Knows
2008
The Wolf at the Door
1986
Vagabonderne paa Bakkegaarden
1958
That Brief Summer
1976