According to officials, more than 70 others were injured as the blast hit the San Pablito fireworks market in Tultepec, about 20 miles outside Mexico City.
Footage from the scene showed a large number of fireworks rocketing into the air as they caught fire.
Dozens of paramedics and police attended the scene. The cause of the explosions is not yet known.
Locals have been told to avoid the area and keep roads clear.
Eruviel Avila, governor of the State of Mexico, said some children had suffered burns to more than 90% of their bodies and they were being sent to Galveston, Texas, for specialized treatment.
Most of those killed are so badly burned their bodies will have to be identified using DNA testing, Eruviel Avila added.
According to Mexican media, fireworks continued to explode after the initial blast, as smoke billowed from the area in thick black clouds. The market had contained up to 300 tones of fireworks.
Photos from police and medical personnel at the scene showed several injured people among the destroyed market stalls, with brick buildings scorched by the heat.
President Enrique Pena Nieto tweeted condolences to the families of the victims and wished a speedy recovery to the injured.
He also said members of the defense forces were assisting in the emergency.
In 2005, the San Pablito market was heavily damaged by similar fires, when a chain of explosions just before Mexico’s Independence Day celebrations injured dozens of people.
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