Interior Ministry spokesman Saad Maan Ibrahim said in one of the attacks near the heavily fortified area a suicide bomber targeted a security checkpoint by striking a restaurant often visited by Iraqis going into the Green Zone, CNN reported.
A second blast occurred near Iraq's Foreign Ministry building, officials said. Witnesses said a car bomb exploded while the Interior Ministry said it was a suicide explosion.
The third blast occurred in one of Baghdad's main commercial areas.
At least 30 people were injured in the bombings. Police officials did not break down how many people were killed or injured in each instance, CNN said.
The United Nations said 2013 was the deadliest year in Iraq since 2008, with nearly 8,000 people, mostly civilians, killed in the violence.
The U.N. mission in Iraq said 618 civilians and 115 members of the country's security forces were killed in violence or acts of terrorism in January. The U.N. figure doesn't include the violence that has swallowed Anbar province, where al-Qaida-connected militants and Iraqi security forces have been fighting since the end of last year.