A tweet posted to the account OpCharlieHebdo (Operation Charlie Hebdo) said “Tango Down” and included a link to the website ansar-alhaqq.net, which has been linked to extremists.
The attack is the first success for Anonymous after the group posted a video last week saying it would target extreme social media accounts as part of efforts to protect freedom of speech.
The warning came in the same video as a tribute to the victims of the attack on French satire magazine Charlie Hebdo.
On Sunday, more than a million people marched through the streets of Paris, as well as at separate gatherings in London and other cities around the world in a show of solidarity following the terrorist attack, in which 12 people were killed.
A Belgian segment of the hacking group said in the message: “We are declaring war against you, the terrorists.” Since it was posted on January 8, more than 6.5 million people have watched the clip, which shows a figure wearing the group’s signature Guy Fawkes mask.
In an earlier message posted on forum site Pastebin, the group addressed the “enemies of freedom of expression”, and warned extremists: “Expect a massive frontal reaction from us because the struggle for the defence of those freedoms is the foundation of our movement.”
The message signed off by saying: “We will not forget. We will not forgive. Dread us.”
The nature and type of attack on the website is not yet known, but in the past Anonymous has used Distributed Denial of Service (DDoS) as a way of bringing down websites by flooding them with traffic until they go offline.
DDoS attacks were identified as the source of the problems with the Playstation Network, which went down over Christmas leaving gamers unable to get online.