The depot, run by a militia group under the umbrella of the Iran-backed Popular Mobilization Forces, was located inside a federal police base in the southern suburbs of Baghdad.
The facility stored short-range and Katyusha missiles, a security source told Reuters.
The fire set off some of the rockets, which struck neighborhoods several kilometers (miles) away and injuring mainly children, said Qasim al-Attabi, a spokesman for the district’s health directorate.
Health Ministry spokesman Saif Badr said most of the wounded were discharged from area hospitals with light wounds.
A police source said the fire was probably caused by negligence leading to poor storage conditions and high temperatures. The Interior Ministry ordered an investigation.