In a video posted on YouTube, a man wearing a Guy Fawkes mask described the jihadist militant group as "vermin" and vowed to hunt them down.
"We are going to launch the biggest operation ever against you. Expect many cyberattacks. War has been declared. Get ready," the man said in French.
"We don't forgive and we don't forget."
The promise to unleash waves of cyberattacks on "Islamic State" (IS) came after the jihadi militants claimed responsibility for a series of bombings and shootings in Paris on Friday, in which 129 people died.
"These attacks cannot remain unpunished," the man said, without elaborating on what the attacks would involve.
Echoes of 'Charlie Hebdo'
Anonymous is an international network of activist computer hackers, which has claimed responsibility for several cyberattacks against government, corporate and religious websites over the past 12 years.
The group made similar threats following the fatal attack on satirical French weekly "Charlie Hebdo" in January, and has since claimed to have identified more than 39,000 suspected IS profiles and reported them to Twitter.
It also claims to have had more than 25,000 of these accounts suspended, while almost 14,000 others targets remain active.
ksb/cmk (Reuters, AFP)