In attacks in other parts of the country, a car bomb was detonated at a market in the city of Suweira, Kut province, killing eight people and injuring 29 more.
A suicide bomber targeting a police checkpoint also killed two people in the northern city of Mosul. While another 10 police officers were wounded in the western city of Fallujah on Monday after bombs were planted outside their homes.
The attacks, executed within hours of each other, showed a new tactic being used by anti-government fighters in the country, Reuters news agency quoted an interior ministry spokesman as saying.
"This was a message to us that they can attack us in different parts ... at the same time because they have cells everywhere," he said.
The attacks come just two days after reports that the Iraqi defence ministry was considering building a "security fence"around the capital as a way of curbing violence and controlling the movements of anti-government fighters.
Access to the city would be controlled by eight checkpoints, and construction could be completed by mid-2011, reports from local broadcaster Al Iraqiyya Television said.
Violence across Iraq has dropped significantly since 2006 and 2007, when the country's sectarian conflict was at its height. But attacks have been on the rise in recent months, particular in Baghdad.
National parliamentary elections on March 7left no clear winner, and continuing wrangling by political blocs to form a governable coalition have left an atmosphere of instability in the county.
Security forces have in recent weeks also made a series of arrests of high-profile members of the al-Qaeda in Iraq group, Al Jazeera's Mike Hanna, reporting from Baghdad, said.
"Certainly, authorities were predicting a backlash against that, we had seen a number of attacks recently, but this is the most serious in terms, not only of the death toll, but of the sense of co-ordination," he said.
"It would be a very strong answer, if indeed it is an al-Qaeda group [behind Monday's strikes], that despite the fact that their leadership is gone, they are still capable of carrying out this type of attack."
Police said three of checkpoints fired at on Monday were in the west of Baghdad, with two more in the east and one in the south. The checkpoints that were bombed were in the south and southeast of the capital.