In the first attack, a car detonated on a commercial street in the Meshtal neighbourhood in eastern Baghdad, killing at least eight people and wounding 15, police officials said.
The second car bombing took place in Baghdad's western Amiriya district, also hitting a commercial street and killing at least six people and wounding 16 there.
Hospital officials confirmed the casualties. All spoke on the condition of anonymity because they were not authorised to talk to media.
The Sunni militant group has claimed responsibility for a number of attacks in the capital, including one on Sunday, when an online statement claimed a bombing at a checkpoint outside the Baghdad International Airport. Five people were wounded in that attack.
No one immediately claimed responsibility for either of today's blasts.