A car bomb exploded near a restaurant and shopping area in the central district of Karrada late on Saturday.
The street was busy with shoppers after sundown in the holy month of Ramadan, which ends this week.
A second bomb exploded later in a predominantly Shia area north of the capital, killing another five people.
The bombings, among the deadliest in Iraq this year, come a week after Iraqi security forces recaptured the city of Falluja from Islamic State (IS) militants.
Authorities say the city was used as a launching pad for attacks on Baghdad by IS.
The jihadist group on Saturday claimed responsibility for the car bomb in Karrada in a statement distributed online by supporters of the hardline Sunni group.
There are reports the source of the blast was a refrigerator van packed with explosives.
Many of those killed in the attack, close to midnight, were children, Associated Press reported.
It caused a huge fire on the main street. Several buildings were badly damaged and were still on fire early on Sunday.
Prime Minister Haider al-Abadi visited the scene in the morning, and was met by angry crowds.
IS still controls large swathes of territory in the country's north and west, including Mosul, Iraq's second largest city.
But the group has been under pressure in Iraq and in neighbouring Syria, where it has been targeted by government forces and US-backed rebels.
This latest deadly attack took place in the central Karrada district before dawn, when Iraqis, like many Muslims in the Arab world, gather in large numbers in juice bars and cafes to have their meal before they start another day's fasting in the holy month of Ramadan.
Angry residents chased the convoy of the Prime Minister Haider al-Abadi with stones and bricks when he tried to visit the scene of the carnage few hours after the explosion.
The also vented their anger online. Hackers broke into the website of the Interior Ministry and placed a gruesome picture of a killed child and a drawing of a fake bomb detector, one of the useless devices that are still in use in Baghdad at checkpoints, through which car bombs and suicide bombers pass.
