In one attack, a car bomb went off near a church during Christmas Mass in the capital's southern Dora neighbourhood, killing at least 15 people and wounding more than 30, a police officer said.
A little bit earlier, a bomb ripped through an outdoor market in the nearby Christian section of Athorien, killing seven people and wounding 16, the officer added.
There was no immediate claim of responsibility for the attacks, but Iraq's dwindling Christian community, which is estimated to number about 400,000 to 600,000 people, has often been targeted by al-Qaeda and other insurgents who see the Christians as unbelievers.
A medical official confirmed the casualty figures. Both officials spoke on condition of anonymity because they are not authorised to talk to the media.
Today's 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 Iraq in the past months, sending violence to levels not seen since 2008.