The two blasts went off within minutes of each other in the city's crowded al-Karkh area. One of the cars had been parked near the government office where identity cards and passports are issued, while the other had stood alongside a branch of the Iraqi Commercial Bank.
The government office was open for business Sunday, with many people inside the building.
Members of the Iraqi police force were among those killed in the blasts, security sources said.
The death toll is likely to rise given the severity of the injuries suffered by some victims, sources added.
Iraqi security forces cordoned off the area, while ambulances transferred the injured to a nearby hospital.