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6 year oldThe biggest blasts took place as police and fire fighters arrived at the scene in the town of Tultepec. Emergency workers are among the casualties.
Video on social media shows a huge cloud of smoke over the site in Tultepec.
The town, about 30km (20 miles) from Mexico City, is known as the country's pyrotechnic capital.
A market in the town has twice been badly damaged by explosions. More than 40 people died in blasts there in 2016.
At the time there were calls for the market to be closed, but President Enrique Peña Nieto promised to rebuild it and help hundreds of local artisans who had lost their livelihoods.
An explosion earlier this year killed seven people.
Tultepec hosts Mexico's national pyrotechnics festival each year.
The latest incident began at about 09:30 local time (14:30 GMT). Local people described the scene.
"I was having breakfast when there was a terrible blast. We left the house running and I saw a huge white cloud in the sky, as if it were going to rain - except today it rained fire," said resident Alondra Perez, quoted by the AFP news agency.
The government of Mexico state said in a statement: "Emergency crews attended the call of the first explosion, when a second incident occurred, killing and injuring members of these groups."
At least four workshops were destroyed, local media said. A fire triggered by the blasts was said to have been brought under control.
Firework accidents are common in Mexico, not least in Tultepec:
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