Three people were killed in the blasts, which came within 20 minutes of each other at four churches and the Vatican mission in Baghdad, and two other churches in the northern city of Kirkuk.
No one has claimed responsibility for the attacks.
The council of Iraq's top Shi'ite leaders, the Najaf Hawza, condemned the bombings and called for cooperation between the country's religious and ethnic groups.
The Sunni-based Iraqi Islamic Party called on the government to provide holy places with protection.
The papal nuncio to Iraq, Monsignor Fernando Filoni, said the attacks were intended to intimidate Iraq's small Christian community.