Militants blew up a car bomb in front of a house used by Iranians as a rest stop in the Kadhamiya district of Baghdad, as well as explosives planted in an adjacent house, an Interior Ministry source said.
The explosions killed five people, wounded 18 and severely damaged the two houses, the source said.
In Baghdad's northern Shula district, a car bomb exploded near a bus carrying Iranians, killing two people and wounding 28, the source said.
A police source said seven were killed and 45 wounded in total in the two incidents.
A third car bomb blast struck a market in Baghdad's southwestern Bayaa district, killing six people and wounding 41 others, the ministry source said.
Baghdad's northern Kadhamiya area hosts the golden-domed shrine for Imam Moussa al-Kadhim, a medieval Shiite holy man. During a pilgrimage in 2005, rumours of a bombing on the Bridge of the Imams, which leads to the shrine, touched off a stampede that killed 1,000 people.
Hundreds of thousands of Iranian religious tourists have visited Shiite holy sites in Iraq since the 2003 U.S.-led invasion that toppled Saddam Hussein.
Saddam crushed insurrections by Iraq's Shiite majority, banned Shiite religious festivals and fought an eight-year war with Shiite power Iran.
Pilgrims are often targeted by Sunni Islamist groups such as al Qaeda in Iraq, which view Shiite Muslims as apostates.
Fifteen people died and dozens were hurt on Friday when two buses carrying mostly Iranian pilgrims collided on a highway near the city of Hilla, about 100 km (62 miles) south of Baghdad. Number of people killed in violence in Iraq last month was the lowest in a year for the second month running, with 171 people -- 105 civilians, 23 soldiers and 43 policemen -- dying in attacks.