It was later reported that another five people had died in the hospital.
The blast happened in a house in Chilcotla, Puebla state, which was being used as a warehouse to store fireworks ahead of a local festival next week. Numerous victims were inside the two-story house, which was leveled by the blast.
El Universal cited local officials as reporting someone threw a lit firework that landed inside a building behind the local church where the pyrotechnic materials for the celebration were being stored, causing a blast that seriously damaged the structure.
It comes just months after 31 people were killed at a fireworks market in Tultepec, Mexico.
A series of massive explosions destroyed a fireworks market outside the Mexican capital in December, killing at least 35 people, injuring dozens and leaving the market a charred wasteland.
State governor Antonio Gali Fayad, who plans to visit the scene of the accident, expressed his condolences overnight as the scope of the tragedy became clear.
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The dinner is an annual celebration of journalists and media members and is sometimes jokingly called "Nerd Prom" by attendees. At one point Minhaj mocked Trump by saying that the president looks like he'd been roasted for 70 straight years.
The fireworks explosion in San Isidro, a village 170 miles east of Mexico City, is the second incident in recent months.
Investigators believe a rocket exploded at that market and set off a chain reaction of other blasts.
Mexico and many other Latin American countries often use fireworks as part of celebrations throughout the year.
In that catastrophe, the sky filled with multicolored smoke as the San Pablito market echoed with the crack and thunder of exploding fireworks.
The market was filled with people shopping for Christmas and New Year's festivities.
The fireworks industry brings in almost $10 million a month in revenue in Mexico, authorities say.