The California-based company had tried to have the girl’s claim thrown out.
But a High Court judge in Belfast rejected the social media giant’s argument.
The girl’s lawyers allege that the photo was obtained through blackmail and then repeatedly posted online, between November 2014 and January this year.
The girl, who cannot be named for legal reasons, is seeking damages for misuse of private information, negligence and breach of the Data Protection Act.
She is also suing the person who allegedly posted the photo.
Her lawyers argued that Facebook could use a “fingerprinting” technology to prevent the photo being re-uploaded.
In response, Facebook argued that European law did not require it to sift through vast amounts of material uploaded online, and that it had removed the picture whenever it was notified.
Facebook has had a difficult time in policing content on its platform recently.
Last week, a Norwegian newspaper dedicated its front page to a decision by Facebook to remove a celebrated photo of a nine-year-old girl running from napalm in the Vietnam War.
Facebook said the photo violated its community standards on nudity.
The Norwegian Prime Minister Erna Solberg posted the same image, which was also removed by Facebook.
Facebook later reinstated the post.
Facebook’s chief operating officer, Sheryl Sandberg, wrote to Ms Solberg, saying: “These are difficult decisions and we don’t always get it right.
“Nonetheless, we intend to do better.
“We are committed to listening to our community and evolving.
“Thank you for helping us get this right.”
Facebook did not respond to immediate requests for comment.
News Source SkyNews