According to the UniradioInforma news portal, citing the boy's mother, he was injured while playing a kite with his younger brother in the yard.
Police officers took the injured child to a nearby private clinic, but doctors could not save him, the news portal added.
The incident reportedly took place after the criminal robbed a store and tried to hide from the police in an empty lot next to the boy's house, opening fire at them. The bullet could have been fired both by the criminal who died in the shootout and by the employees of the Tijuana municipal police.
The city mayor, Arturo Gonzalez Cruz, expressed his condolences to the child's family, which demands justice, as well as expressed the hope that prosecutors would establish those responsible for the crime. Four police officers were suspended from service during the investigation.