The blasts came hours after at least 41 people were killed in a Sunni area of the Iraqi capital by militia members who set up a fake checkpoint.
Police and interior ministry officials have accused the al-Mahdi army militia, run by Moqtada al-Sadr, the Shia cleric, of involvement in the killings.
Mahdi army militia have any denied involvement in the deaths.
"I urge all government and popular forces to exercise restraint and take responsibility in front of God first and society secondly," al-Sadr said in a statement on Sunday.
He blamed Sunday's violence on a "Western plan aimed at sponsoring a civil and sectarian war between brothers".
Nuri al-Maliki, the Iraqi prime minister, has vowed to disband the militias, many of which have ties to political parties.