The attacks happened the same day anti-ISIS forces advanced on the terror group's stronghold in Mosul.
The first blast happened when a driver blew up his explosives-laden vehicle at the Alwat-Jamila market in eastern Baghdad's Sadr City. At least 11 people were killed and 25 were wounded, police said.
In the second attack, a suicide bomber wearing an explosive vest blew himself up at a busy market in the eastern Baghdad neighborhood of al-Baladiyat, police said. At least five people were killed, and 12 were wounded.
ISIS' media wing, Amaq, claimed responsibility for both explosions in statements posted on Twitter. The statements said the bombings targeted Shiites.
Car bombs and roadside bombs are not uncommon in Baghdad, but in 2017, ISIS has already carried out several attacks across the capital and killed dozens of people.
Iraqi forces move in on Mosul
The latest wave of violence in Baghdad came as Iraqi counterterrorism forces reached the east bank of the Tigris River in eastern Mosul on Sunday, Lt. Gen. Abdul Amir Rasheed Yarallah said in a statement.
Iraqi security forces on Sunday killed more than 125 ISIS militants in several neighborhoods in eastern Mosul, according to a statement released by Iraq's joint operations command.
Forty ISIS fighters were killed by counterterrorism forces as they were advancing toward the east bank of the Tigris River, the statement said, with the US-led coalition providing air support.
The Iraqi army, counterterrorism forces and fedral police have been battling ISIS in eastern Mosul since the second phase of the Mosul operation was launched about 10 days ago.
Their progress marks the first time Iraqi troops were able to reach the river since large-scale military operations to root out ISIS started in the Mosul area on October 17, 2016.