The source said that one of the bombers blew themselves up in Tayaran Square, while the other detonated their device in the "Bab al-Sharqi" market in central Baghdad.
The source noted that ambulances had rushed to the scenes of the explosions to transport the dead and the wounded to nearby hospitals.
According to police sources, the death toll could increase as some of the wounded were in critical condition.
As the explosions occurred in a commercial center in central Baghdad and besides human casualties, material damage was reported.
The Iraqi security services cordoned off the two bombing sites, while also reportedly closing the entrance to the Green Zone, occupied by the federal government as its headquarters in central Baghdad.
No group has claimed responsibility for the attacks yet.