A statement from Cumbria police explained emergency services had been called to reports a child had been seriously injured by a firearm at bout 2:50pm yesterday (28 September).
Police and North West Ambulance Service attended the farm in the Warcop area.
“Sadly, the boy has died overnight.”
Cumbria Police are now investigating the boy’s death.
A man in his 60s was arrested at the scene on suspicion of assault GBH.
“He remains in police custody but is now under arrest on suspicion of gross negligence manslaughter,” the force added.