Those explosions killed at least 12 people, including three policemen, and wounded 22, a police officer said.
Shortly afterward, a suicide bomber walked into a nearby falafel restaurant where he set off his explosives-laden belt, killing five people and wounding 12, the officer added.
The restaurant and others around it are often used by officials or visitors waiting for security escorts to take them inside the Green Zone.
Also today morning, a parked car bomb went off in Khilani Square in the Iraqi capital's commercial centre, killing five people and wounding 11, another police officer said.
Security forces sealed off the area as firefighters struggled to put out the blaze ignited by the bombing.
Smoke billowed from several stores and stalls as some vendors hurriedly stuffed their goods into big bags and carried them away on their backs.
