The incident took place in the Virudhunagar district, the NDTV broadcaster reported on late Friday.
"Friction during mixing of chemicals appears to have caused the explosion," an officer from the local fire department told NDTV.
Indian Prime Minister Narendra Modi has expressed condolences over the deadly explosion.
"Fire at a firecracker factory in Virudhunagar, Tamil Nadu is saddening. In this hour of grief, my thoughts are with the bereaved families. I hope those injured recover soon. Authorities are working on the ground to assist those affected," Modi wrote on his Twitter page.
The Indian government will pay some $2,700 to families of the deceased people and $678 to those of the injured people.