Cybersecurity firm Sixgill revealed the shocking threats as part of a wave of online terror operations by the so-called United Cyber Caliphate (UCC).
ISIS is circulating images featuring Zuckerberg in an orange jumpsuit and beheaded - including the message “Go to hell Mark”.
Jihadis are ramping up their hacking operations as part of a campaign the terrorists have dubbed “#OpTheWorld”.
Numerous websites have been targeted - and successfully attacked - experts from Sixgill revealed to Daily Star Online.
Included in a dossier of their findings is claims from ISIS that they have successfully hacked numerous accounts on Facebook as part of their "vendetta'.
Sixgill revealed “several pro-ISIS” hacking groups have begun to work together as the UCC.
UCC’s activities have “intensified” since late May - with at least seven government websites being successful hacked in East Asia.
Tens of others have also been brought down in DDoS attacks which overwhelm websites with users - forcing them offline.
Facebook appears to be their biggest target, with propaganda calling for hackers to assault the social media site in the same way other ISIS wings call for terrorist attacks.
Zuckerberg appears in one propaganda poster having been mocked up in an orange jumpsuit.
He sits on his knees with his head severed by an identified black-clad executioner wielding a sword.
It includes the Facebook logo with a red “hacked” message plastered across it - accompanied by the hashtag #OpTheWorld.
ISIS has also been circulating screenshots, which claim to show dozens of successfully hacked Facebook pages.
Sixgill told Daily Star Online: "We assume that ISIS is targeting Facebook to retaliate against its measures to censor pro-ISIS content and groups, and on more general level because Facebook is seen as a Western symbol.”
UCC claimed ISIS hackers had successful hacked 213 websites and downed 520 websites in a message circulated on July 9.
Experts from Sixgill added ISIS appears to have “vendettas” against certain individuals and groups - including Zuckerberg and Facebook.
ISIS also threatened online activist group Anonymous - warning them “this is what happens if you continue to challenge us”.
ISIS has been on the run since their strongholds in Iraq and Syria were liberated over the past two years.
Jihadis are now being driven underground, pumping out propaganda calling for attacks on the West.
Terror threat warnings the UK remain at “severe” - meaning an attack in “highly likely”.
And this month, a most wanted ISIS executioner was killed in a gunfight after he was involved in the burning alive of to two Turkish soldiers.
Source: Daily Star, UK