The men – aged 20, 26 and 41 – were arrested on Sunday on suspicion of possession of a firearm in suspicious circumstances.
It followed the recovery of a shotgun on the Castlewellan Road in Newcastle in the early hours of yesterday morning.
Inspector Lynsey Barr said: “A passing police patrol noticed the men acting suspiciously at around 2 am on Sunday morning.
“And after an examination of the area where they had been standing a shotgun was discovered, concealed in a hedge.
“The three men were arrested a short time later and taken into custody.
“We are investigating a link between this incident and a burglary at a nearby property.
“I would ask anyone with any information to contact detectives at Downpatrick on 101 or Crimestoppers, anonymously on 0800 555 111.”
The men are due at Downpatrick Magistrates’ Court this morning.