One attack struck a busy commercial street in the eastern neighbourhood of Baghdad al-Jadida, police said.
Seventeen people were killed and 43 wounded, mostly civilians, a police colonel said. Hospital sources and an official at the interior ministry confirmed the toll.
At least two people were killed and nine wounded in another attack in Zafaraniya, a district in southern Baghdad, the same sources said.
A huge suicide car bomb attack claimed by the Islamic State group killed dozens of people in Khan Bani Saad, a town just north of Baghdad, on Friday.