The Most Reverend Justin Welby said so-called Islamic State is "igniting a trail of fear, violence, hatred and determined oppression".
He also branded IS as "today's Herods" - a reference to the Biblical king at the time of Jesus's birth.
The archbishop delivered his sermon at Canterbury Cathedral.
He said: "Confident that these are the last days, using force and indescribable cruelty, they [IS] seem to welcome all opposition, certain that the warfare unleashed confirms that these are indeed the end times.
"They hate difference, whether it is Muslims who think differently, Yazidis or Christians, and because of them the Christians face elimination in the very region in which Christian faith began.
"This apocalypse is defined by themselves and heralded only by the angel of death."
The archbishop - spiritual leader of the world's 85 million Anglicans - also said that to those who have been, or are being, "dehumanised by the tyranny and cruelty" of IS, then "God's judgment comes as good news, because it promises justice".
Referring to IS as Isis, he told the congregation: "Today's Herods - Isis and their like - around the world propose false apocalypses.
"But you and I are called this morning to respond in worship and transforming, world-changing obedience, both as individuals and together, to this revelation of the baby that defines God.
"For it is our response to Jesus that defines us."
He has also tweeted: "In our world today extremists talk of coming apocalypse: it's already happened - in newborn Jesus, God radically reimagined the world.
"The apocalypse of Christmas judges every power, reaches every refugee and asks us all how we respond to Jesus, Prince of Peace."
Cardinal Vincent Nichols, Archbishop of Westminster and the head of the Roman Catholic Church in England and Wales, used his homily at midnight mass to say in a life shaped by faith in God, there is "absolutely no room at all for gratuitous violence".
He said: "No to all violence against the innocent. Yes to mercy. If we learn those lessons, then our world and our families will be more graceful places... and then, you and I can be protagonists of unarmed goodness."
The archbishop added that he hoped Christians who had been forced to leave their homes in northern Iraq would find some comfort from the Christmas story.
"I think many a Christian who's been driven from their home, who's seen family members killed, who knows of relatives who are in great distress, will draw great comfort from this feast and from the knowledge that their plight is being talked about throughout the world," he said.
Elsewhere, Chief Rabbi Ephraim Mirvis, in his own message for the festive season, will condemn "aggressive secularism that threatens to relegate spirituality and sanctity within our society" as well as the "shameful scourge of hatred and oppression, which remains the most pressing global challenge of our time".
The Anglican Archbishop of York visited an open prison in North Yorkshire on Christmas Day to lead morning services. Dr John Sentamu attended Kirklevington Grange Prison, where he told inmates that it is never too late for a fresh start.
Christianity faces "elimination" in the Middle East, the region where it began, the Archbishop of Canterbury has warned in his Christmas Day sermon.