The car bomb killed at least 24 people, most of them Christian, when worshippers were leaving the church in the Doura district of southern Baghdad, police sources said.
No one immediately claimed responsibility for the attacks.
Violence in Iraq has risen to its worst levels in more than five years as hardline Sunni militants linked to al Qaeda step up attacks on the Shi'ite-led government of Prime Minister Nuri al Maliki and anyone seen as supporting it. Many thousands have been killed in attacks this year.
The minority Christian community has been a target of attacks by al Qaeda militants in the past, including a 2010 attack on a church that killed dozens of people.
Two bombs also went off in a crowded market in a separate, mostly Christian area in Doura, killing another 10 people, police and medics said.
At least 52 people were wounded in the attacks.
A series of car bombs, shootings and suicide attacks killed scores of Shi'ite Muslim pilgrims in the week before the Shi'ite holy day of Arbaeen, which coincided with Christmas Eve this year.
The bombings came amid a massive military operation in Iraq's western desert as authorities try to hunt down insurgents who have stepped up attacks across the country in the past months, sending violence to levels not seen since 2008.
The Christmas Day attacks brought the total number of people killed so far this month in Iraq to 441.