Authorities at Broken Hill's hospital have described the arrest of staff member Jonda Stephen for allegedly stabbing a man to death as "very sad."

The incident happened at a house on hospital land on Chloride Street on Monday evening.

Officers say they found 57-year-old Christopher David Tiffin with a stab wound to his chest outside the house when they were called to the address just before half past 7 on Monday night.

They arrested a 48-year-old Stephen at the scene, who had cuts to her face.

Mr Tiffin was taken inside the hospital but died a short time afterwards and police charged the woman with murder.

Inspector Mick Stoltenberg from the police says the alleged stabbing involved a domestic dispute.

"I can confirm that it is domestic-related and I won't go into it any further than that at this time," he said.

"It's still obviously very early stages in our enquiries and our investigations, and it's also the case that next of kin have not been notified."

Police say Stephen, who has been charged with murder, is an employee at the hospital.

"This is a very sad occasion for all concerned, and support is being offered to all staff affected," a hospital spokesman said.

"It is a police matter and it would be inappropriate to comment any further."

The hospital's offering counselling to staff.

The victim is known to police but the woman is not believed to be.

She appeared in court on Wednesday and refused bail to appear in court again in December.