The head of the Church, Patriarch Louis Raphael Sako, said the decision was made out of respect for those killed and wounded in recent anti-government protests, which have now been going on for three months.
"There will be no decorated Christmas trees in the churches or streets, no celebrations and no reception at the patriarchate," he said in a statement on Tuesday.
Almost 430 people have died and 20,000 wounded in mass rallies that have been met with retaliation by security forces.
The protests have mostly being taking place in Shia Muslim-majority areas, but the Church said it would take part in an act of solidarity "out of respect for the dead and wounded among protesters and security forces, and in solidarity with the pains of their families".
Iraq's parliament formally accepted the prime minister's resignation on Sunday,
Protesters are calling for a complete overhaul of the sectarian political system.
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