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 ten 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.