"The latest reports said that 23 people were killed and 59 injured in the twin bomb attacks in Mreidy Market in Sadr City district," Xinhua cited sources as saying.
The incident occured when a booby-trapped motorcycle went off at the crowded popular marketplace in the predominantly Shia district of Sadr City in eastern Baghdad, the source said.
Minutes later, a suicide bomber blew up his explosive vest at the scene, the source added.
The powerful blasts destroyed several nearby shops and many stalls and set fire to several civilian cars, he said.
The attackers apparently followed the old tactic of first creating an initial explosion to attract security forces and people, and then setting off another blast to inflict heavier casualties.
Earlier, a UN report estimated more than 22,300 people were killed or injured in armed conflicts in Iraq in 2015.