The shooting happened in Detroit yesterday when the girl was playing with the boy in a home on the city's west side.
There were three children -- all cousins -- at the home at the time of the incident, said Detroit Deputy Chief Rodney Johnson. The third child was 5, he said.
The children found a "long gun" under a bed, pulled it out and began to play with it, Detroit Police Public Information Officer Adam Madera said.
There was an adult present in the house but that person was a family friend and unrelated to the children, Johnson said.
"It's too early to say if charges will be filed in this case," Johnson said.
This is the latest incident involving children who accidentally shoot someone or die of a self-inflicted gunshot wound.
In October, a babysitter in Vidor, Texas, was charged after a 5-year-old toddler she was looking after fatally shot himself with her gun, police said.
In New Orleans, a 5-year-old girl died on June 23 after she came into contact with a .38-caliber revolver and accidentally shot herself in the head while her mother was at a store, police said.
Last August, a 3-year-old boy in Dundee, Michigan, found a .40-caliber handgun belonging to a family friend on a closet floor in his home. He died after accidentally shooting himself in the head, police said.
A study of Colorado trauma center data found a surprising number of children were being injured, many of them seriously, by guns.
During the same period, 7,766 children under the age of 14 suffered accidental firearm injuries.
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