He has been named locally as Aaron Macaulay.
The incident happened at a property on the Rathfriland Road on Tuesday afternoon.
According to a spokesperson for the Northern Ireland Ambulance Service, the boy fell from farming machinery shortly before 2.30pm.
Two paramedics accompanied him as he was airlifted to Craigavon Hospital.
A PSNI spokesperson has confirmed his death.
The NI Health and Safety Executive are currently investigating.
A spokespersons said: "HSENI is investigating the death of a 10-year-old boy on a Co Down farm. Our deepest sympathies are with the family at this most difficult time."
Aaron's older brother Matthew, who's believed to be in his late teens, was also injured in the accident and is recovering in hospital.
His parents Maurice and Wendy are said to be devastated at what's happened.
Local politicians have led the tributes.
South Down SDLP MP Margaret Ritchie said: "This is a terrible tragedy and my sympathies and condolences are with the family, friends and local community who I am sure are in a state of distress following their terrible loss."
Danny Kennedy, UUP Newry and Armagh MLA, who knows the wider family circle, said: "My thoughts and prayers are with the family of the young boy who died in this latest farm tragedy.
"I know the wider family circle and they are very well respected in the local community.
"I hope that they will find strength and comfort in the coming days to help them in the wake of the loss of their young son. This was an awful tragedy and we must give the family time and space to get through the coming days."
South Down NI21 MLA John McCallister said: "My thoughts and prayers are with the family. This really is a tragic event."
Alliance Newcastle councillor Patrick Clarke said: "I would like to offer my heartfelt condolences to his family. This must be an extremely difficult time for them. There are no words to describe the pain they must be feeling after their loss."
Barclay Bell of the Ulster Farmers' Union said: "The farm is also a family home and that may be part of the difference. It is another loss of life and a small child so certainly it is not good news for the wider farming family in Northern Ireland.
"I still think the whole farming community, the families on farms, they really have to try hard and challenge the mindset a bit, that they just need to stop and reassess and think 'can I do this any safer, can I make my farm safer in general'?"