Near-simultaneous explosions went off near a mosque close to the Diyala bridge in southern Baghdad shortly afterwards, killing four people and wounding 17 others.
'Enemies of Iraq'
The other blasts struck worshippers in the southeastern neighbourhood of Zafaraniyah and the eastern district of Kamaliyah.
There was no immediate claim of responsibilty for the blasts.
"Those who carried out these acts targeting the faithful are the enemies of Iraq, without principles or values," Reuters quoted Major-General Abboud Qanbar, the head of Iraqi forces in Baghdad, as saying.
The attacks came a month after US troops pulled out of Iraq's towns and cities.
Violence has dropped markedly throughout the country in recent months, but attacks increased in the run-up to the US pullback.
US commanders have warned that security gains made in the last year are fragile and reversible, and they have said attacks may escalate ahead of national elections next year.
More than 430 Iraqis were killed in June alone, which is the highest death toll for 11 months.
Attacks remain especially common in Baghdad.