The blasts took place in mainly Shiite districts of Iraq's capital, Voice of America reported.
The total number of bombs wasn't reported.
The first car bomb killed three people and injured 17 others, an Interior Ministry source said, as reported by China's official Xinhua News Agency.
The bomb was inside a parked car at the busy Mreidy market in Sadr City district in the eastern Baghdad, the source said.
"The security forces and the ambulances hurried to the explosion area and transferred the injured to the hospital for treatment and the dead (to) the morgue," a security source, whose name wasn't reported, told IraqiNews.com.