She claims that since 2009 they have made her life a misery by constantly posting hundreds of photos of her, including embarrassing and intimate images from her childhood.
Legal expert Michael Rami was quoted by Austrian media as saying he believes she has a good chance of winning in court.
The shared images include baby pictures of her having her nappy changed and later potty training pictures.
"They knew no shame and no limit - and didn't care whether it was a picture of me sitting on the toilet or lying naked in my cot - every stage was photographed and then made public,” the 18-year-old said. The photos were shared on Facebook with her parents' 700 friends.
Despite her requests, they have refused to delete the photos - prompting her to sue them. "I'm tired of not being taken seriously by my parents", she said. Her father believes that since he took the photos he has the right to publish the images.
Rami says that if it can be proven that the images have violated her rights to a personal life, then her parents may lose the case. This is the first case of its kind in Austria, but he says that based on similar cases abroad the girl's parents may have to pay some financial compensation for her pain and suffering, and will also be liable for her legal costs.
The case will be heard in November - and if the parents lose this could have repercussions for Austrians who post countless images of their children on social media without their consent.
Austrian privacy laws when it comes to social media are not as strict as some other countries - for example in France, anyone convicted of publishing and distributing images of another person without their consent can face up to one year in prison and a fine of up to €45,000. This would apply to parents publishing images of their children too.
French authorities have warned parents against sharing photos of their children on Facebook, saying that the images could attract sexual predators and warn that children could face social and psychological problems later if intimate and embarrassing photos are shared with a wider public.
Subsequently, some doubts have been expressed about the veracity of this story.