CBS News Correspondent Kimberly Dozier, who is in the capital, says many locals were saying Friday's in the capital's Mansour section was really aimed at a church near where the explosion occurred, but the driver took a wrong turn.
Churches this year have announced that the traditional Christmas services will be canceled and replaced by brief early morning prayers. Receptions for parishioners and other festivities were also called off.
The holiday comes just five weeks before next month's key legislative elections, which insurgents have sought to disrupt with a series of bloody assaults across Iraq.
In Baghdad's predominantly Christian southeastern neighborhood of Karada, only about a dozen people showed up for morning Mass at the Notre Dame de la Deliverance Church. Plainclothes guards armed with guns stood outside the church.
Inside the church, apprehensive worshippers lit candles as priests gave communions.
Services in other churches in Baghdad also had humble attendance, and hotels and shops in Christian neighborhoods did not hang holiday decorations as they usually do.
Representatives of rebel Shiite cleric Muqtada al-Sadr visited a church in the upscale Mansour neighborhood in a sign of solidarity with the Christian community. Ibrahim al-Haidary, an al-Sadr aide, told the congregation that the group is willing to post its militiamen to protect churches.
Islamic militants have regularly targeted members of Iraq's varied religions, including the country's 700,000 Christians, in a bid to foment sectarian tensions and disrupt the reconstruction of the war-scarred country.
Churches were bombed in August, September and October, prompting many Christians to flee to neighboring Jordan and Syria. The August attacks hit four churches in Baghdad and one in Mosul, killing 12 people and injuring 61 others.