Until 1985, she was married to the jazz musician, Holger Laumann, with whom she has two children; Eva (Evamaria) and Jan Martin (Sean), now named Marcus.
She is also the mother of Alexander Theo Linnet, whom she had with Mads Buhl Nielsen. Alexander followed a musical life like his mother and is known as Xander and his single "Det burde ikk være sådan her" topped the Danish Singles Charts in 2011.
Linnet also has two adopted children, Peter and Maria.
She is a bisexual and has had both male and female lovers, and has, over time, become a lesbian icon in Denmark.
In 2010, Anne Linnet married Tessa Franck Linnet. In August 2011, Tessa Franck Linnet gave birth to the couple's first child together, a girl named Isolde Elisabeth Franck Linnet.