The first blast struck as worshippers were leaving Friday prayers, while the suicide bomber detonated explosives after security forces arrived.
Security forces members were among the dead and wounded, but the exact number was not immediately clear.
Islamic State has become an existential threat to the West
There was no immediate claim of responsibility for the attack, but extremists, including the Islamic State militant group, often carry out bombings targeting Shias, whom they consider heretics.
The bombings came a week after a series of attacks claimed by IS targeted Shias in Baghdad, killing at least 19 people.
IS overran large areas north and west of Baghdad in June 2014, sweeping security forces aside, and though Iraqi forces have since pushed the jihadists back, the group still holds much of western Iraq.
Islamic State committed genocide in Iraq against Yazidis: report
Bombings in Baghdad have become less frequent since the IS offensive last year, apparently because the jihadists have been occupied with fighting elsewhere.
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