The man, who cannot be identified, started legal proceedings against the social networking site after discovering his photograph and threatening comments had been posted on the page.
High Court judge Bernard McCloskey ruled some content on the page amounted to prima facie harassment of the man, known only as XY.
The man had previously been given a six-year jail sentence for a string of child sex offences committed more than 20 years ago.
Judge McCloskey said "Society has dealt with the plaintiff in accordance with the rule of law.
"He has been punished by incarceration and he is subject to substantial daily restrictions on his lifestyle."
The judge in his ruling gave Facebook 72 hours to take the original page down.
A spokeswoman for Facebook said "We are considering our next steps in light of the court judgment and we have nothing further to add at this stage."
The page, called 'Keeping our kids safe from predators', was no longer visible at 20:00GMT but a new page entitled 'Keeping our kids safe from predators 2' had appeared, gaining over 2,400 likes in just a few hours.
It is not clear whether the creator of the new page is the same as the user that set up the original one.
However, the new page's administrator wrote in a posting at 15:30GMT "Thats (sic) the first page gone ( sad day."
More than 5,000 people had liked the original page before its removal.
Some of the latest posts were written after the judge made his ruling.
Facebook is understood to have removed the man's photo and comments made about him but his legal team insisted that the page should be shut down.
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