Iraqi officials quoted by AP put the death toll from the first attack, in Karrada district, at 86 and said that more than 170 people had been injured.
Interior Ministry spokesman Saad Maan confirmed that the first blast had come from a car bomb.
Eyewitnesses said on Twitter that many shops burned down as a result of the explosions, and there are fears that the number of casualties could grow.
Karrada, an upper middle class district in the Iraqi capital, is mostly inhabited by Shia, but also has quite a large Christian minority. The area becomes very busy after sunset during the holy month of Ramadan.
Shortly after the explosion hit Karrada, eyewitnesses said that a second blast targeted the Shaab neighborhood, which is located in the northern part of the city.
AP said that at least five people were killed in that bombing and another sixteen were injured. Meanwhile, Sky News Arabia said a suspected homemade explosive device was used to hit a market.
Islamic State (IS, formerly ISIS/ISIL) has in an online statement claimed responsibility for the attack in Karrada, Baghdad.
The tactics resemble Islamic State’s signature, as the terrorists frequently choose Shia-populated civilian areas in the capital as targets.
Iraqi security officials are attempting to restore order amid the state of panic that has ensued following the attacks, Altaf Ahmad, a local journalist, told RT.
“Major roads leading to the venue of the explosion [in Karrada] have been cut off. We know that the car bomb that went off in the area that is known to be crowded at this time. After sunset, after the break of fast during the holy month of Ramadan many people start to go out… We are expecting that the number could rise to 100 casualties,” Ahmad said.