Iraqi PM Haider al-Abadi was met by angry crowds while visiting the scene on Sunday. He later declared three days of national mourning.
A second bomb also exploded at about midnight in a predominantly Shia area north of the capital, killing another five people.
The bombing in Karrada is the deadliest in Iraq this year and comes a week after Iraqi security forces recaptured the city of Falluja from Islamic State (IS) militants.
Police said the dead included at least 15 children and six policemen. At least 12 other people were missing, feared dead.
One senior Iraqi official warned that the death toll could rise still further.
The US said on Sunday that the latest attack strengthened its resolve to support Iraqi forces in their fight against IS.
"We remain united with the Iraqi people and government in our combined efforts to destroy Isil," the White House statement said, using another term for the group.
Deadly message from IS: Jeremy Bowen, BBC Middle East editor, Baghdad
The destruction and death adds up to a clear message from the jihadists of so-called Islamic State. They are saying that even if they are defeated on the battlefield, they can still hit back where it really hurts - killing civilians in the centre of the Iraqi capital, and other capital cities, too.
IS have just suffered a serious defeat at the hands of Iraqi forces in Falluja. The town, less than an hour's drive from Baghdad, has been in their hands since early 2014. IS are showing their supporters, and their enemies, that they are not beaten.
So many were killed and wounded because the streets are crowded at night at the end of a day's fasting during Ramadan, with thousands in a mood to celebrate.
It is only realistic to fear that there will be more attacks like this, as IS comes under more military pressure.
In pictures: Baghdad blast
Islamic State group: The full story
IS, which follows its own extreme version of Sunni Islam, said in an online statement that it had carried out the attack.
Iraq's highest Sunni religious body, the Association of Muslim Scholars in Iraq, called the bombing a "bloody crime, regardless of who carried it out or what their motivations were".
GETTY IMAGESThe blast, which struck close to midnight, came from a refrigerator van packed with explosives, reports said.
Many of those killed were children, Associated Press reported. Families gathered on the street on Sunday for news of missing loved ones.
The explosion caused a huge fire on the main street. Several buildings, including the popular al-Hadi Centre, were badly damaged.
Hussein Ali, a former Iraqi soldier, told AFP news agency that six workers at his family's shop had been killed and their bodies so badly burned that they could not be identified.
AFP/GETTY IMAGESMr Abadi visited the scene in the morning, and was met by crowds who shouted "thief" and "dog". Video posted online appeared to show his convoy being pelted with stones.
The BBC's Ahmed Maher in Baghdad says many people are angry at the deteriorating security situation and the fact that IS managed to reach the heart of the capital.
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.
AP9 June 2016: At least 30 people killed in and around Baghdad in two suicide attacks claimed by IS
17 May 2016: Four bomb blasts kill 69 people in Baghdad; three of the targets were Shia areas
11 May 2016: Car bombs in Baghdad kill 93 people, including 64 in market in Shia district of Sadr City
1 May 2016: Two car bombs kill at least 33 people in southern city of Samawa
26 March 2016: Suicide attack targets football match in central city of Iskandariya,killing at least 32
6 March 2016: Fuel tanker blown up at checkpoint near central city of Hilla, killing 47
28 February 2016: Twin suicide bomb attacks hit market in Sadr City, killing 70
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