A judge at the High Court said that some content on the 'Keeping our kids safe from predators' page amounted to prima facie harassment of the man, and risked violating his human rights.
Facebook now has 72 hours to take down the page. In a statement, the social network said that it was "considering our next steps in light of the court's judgements".
The man who brought the case, who cannot be named for legal reasons, was given a six-year jail sentence for child sex offenses committed more than twenty years ago.
The man was found guilty of indecent assault, gross indecency with a child and inciting a minor to commit an act of gross indecency.
Justice McCloskey said that society had "dealt with the plaintiff in accordance with the rule of law", but he is still being punished for his crimes by the harassment.
"He has been punished by incarceration and he is subject to substantial daily restrictions on his lifestyle," he said.
The man issued legal proceedings against Facebook Ireland Ltd after finding his photograph on the 'Keeping our kids safe from predators' page, alongside some threatening comments.
He claimed that he was being harassed, his private information misused and his rights to privacy and freedom being infringed by the page.
The man described the page as an attempt to vilify and stir up hatred against him, and told the court that he feared being attacked or his home being burned down because of it.
Facebook had already removed the man's photos and the comments about him, but his lawyers felt that the page itself should be shut down.
They also asked for a disclosure of the identity of the person or persons who set it up and ran it.
Facebook's lawyers attempted to argue that it was not a proportionate response to remove a page that was followed by 4,000 people.
But Justice McCloskey ruled that closure of 'keeping our kids safe from predators' would only cause minimal disruption to Facebook, and so told the company to shut the page down within 72 hours.