Officers found the dead man's body inside a house at about 4am near the Stuart Highway 350km south of Darwin, NT police said on Thursday.
"It was a confronting scene," Detective Senior Sergeant Jakson Evans told reporters.
"Police located the body of a male person who was deceased from an apparent gunshot wound.
"A male resident of that household was arrested and remains in custody."
Detectives are treating the shooting as a homicide investigation and forensic specialists are examining the crime scene.
The man in custody is 36 years old.
Det Snr Sgt Evans said officers were called to the house after receiving a report there was a male intruder inside the home.
"The residents of the household were home, that's a male and female adult and two children," he said.
The home was located about 30km south of Katherine near the Cutta Cutta Caves Nature Park.
"They are coping as well as can be expected," Det Snr Sgt Evans said of the woman and children.
"We are canvassing the area to see if there were any witnesses."
Investigations continue in a bid to formally identify the dead man and to determine the circumstances leading to his death.
Detectives are also examining whether the incident was linked to an absconder who fled the Venndale Rehabilitation Centre, about 10km south of the caves.
The Venndale facility is a residential drug rehabilitation centre for Indigenous people.
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