The bomb exploded at the Holy Family church in the north of Kirkuk at about 5:30 am (0230 GMT), wounding 15 people including church staff and people in neighbouring houses, the high-ranking officer in the Kirkuk police said.
The officer, who spoke on condition of anonymity, added that 30 homes in the area were damaged.
Imad Hanna, a priest, said it was the first time the church had been targeted.
"Women, children and men from this neighbourhood were wounded in the explosion," he said, added that two of the wounded were in critical condition.
The wounded were taken to Kirkuk General and Azadi hospitals, he added.
An AFP correspondent said that the doors, windows and generators at the church were destroyed, as well as pews inside.
Some cars in the area were also destroyed, he said.
Ethnically divided Kirkuk lies at the centre of a tract of territory which Kurdish leaders want to incorporate in their autonomous region in the north over the opposition of many of the province's Arab and Turkmen residents and of Iraqi Prime Minister Nuri al-Maliki.
The number of Iraqi Christians has dwindled to about 400,000 from an estimated figure of between 800,000 and 1.2 million before the 2003 US-led invasion that ousted Saddam Hussein.
Most of them live in Baghdad, Kirkuk, the area surrounding the northern city of Mosul and parts of the autonomous Kurdistan region in the north of Iraq.
Copyright AFP (Agence France-Presse), 2011