According to al-Sumaria TV, the two bomb attacks targeted Abul Fadhl Abbas (AS) Husseiniya (Shia congregational hall) in al-Maalif district.
Some reports said two suicide bombers had blown themselves up near the center.
According to Al-Arabiya news channel, at least 5 people were killed in the attacks.
No group has so far claimed responsibility for the attacks.
Earlier on Monday, a car bomb was discovered in Al-Na’iriya in northern Baghdad. Police dismantled the bomb before it exploded.