The first bomb was attached to a motorcycle in the market. As the curious gathered to look at the aftermath, a suicide car bomber drove into the crowd and blew up his vehicle.
Authorities said at least three policemen were among the dead.
The blast appeared to target the mainly Shiite neighborhood near the market but also was near the Sheik al-Gailani shrine, one of the holiest Sunni locations in the capital, reports AP.
Raad Abbas, a 26-year-old who received shrapnel wounds in the attacks, said he had gone to the market because the city had been quieter over the past two weeks.
"Shortly after midday, I heard an explosion. Motorcycles were flying in the air, people were falling dead and wounded.
"Some people were trying to help me when I heard the second explosion. The next thing I knew, I woke up here in the hospital," Abbas said from his bed in al-Kindi Hospital.
Malaysia needs Russia's assistance in maintaining and repairing Su-30MKM fighter jets
Posters for the play "Adam and Eve. Life after Paradise" with pictures of dancers Arsen Aghamalyan and Oksana Vasilyeva were banned in the city of Tver, Central Russia