Accounts of the incident differed and it was not immediately clear whether the blasts were accidental or caused by an attack.
The largest blast sent a ball of fire into the sky at a weapons depot used by the Hashed al-Shaabi paramilitary organisation in the Obeidi neighbourhood, on the outskirts of the city.
"The blast took place in a weapons storage facility on a Hashed al-Shaabi base," Ahmed al-Assadi, the organisation's spokesman, told AFP without elaborating.
Several other blasts were reported in nearby neighbourhoods of northeastern Baghdad.
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An interior ministry official said they were caused by rockets but it was not clear whether the rockets had been fired from outside the base or were set off by the fire at the weapons storage facility.
Police and medical officials said at least four people were killed and 16 wounded in the blasts.
The blasts came as tens of thousands of Shiite faithful from across Iraq and abroad converged on the Kadhimiyah shrine in Baghdad to commemorate the death of Mohammed al-Jawad, the ninth Shiite imam.
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