The man, believed to be the husband of a woman missing in South Australia, died by suicide on Wednesday after being told by police that they believed his wife had been murdered.

Officers had been at the 41-year-old man's home near Mannahill, close to the NSW border, to conduct an investigation, police said in a statement.

The man's death came hours after detectives said they believed 23-year-old Tanja Ebert, who had been missing since last week, had been killed.

A commissioner's inquiry has been launched into the incident, a formal process to ensure the incident is investigated thoroughly and independently.

In a statement, police said no one else was injured.

"The man's children are safe and well with family members," the statement said. "A report will also be prepared for the State Coroner."

Ms Ebert was last seen near Roseworthy, north of Adelaide, last week, as she drove home from Adelaide with her husband and her two young boys to the family's pastoral property.

Detective Superintendent Des Bray said her husband told detectives she became agitated in the car and expressed a desire not to return to the family home.

The husband reported she then got out of the car and walked off.

Supt Bray said police now believed Ms Ebert had been killed.

"In the absence of anything to indicate that Tanja is alive, we're treating it as a murder investigation," he said.

"We're hoping for a miracle and she walks through the door, but sadly we don't think that will happen."

Her husband did not report her missing when she left the car last week, with police only notified of her disappearance by a family member two days later.

Supt Bray said it was known Ms Ebert, who had come to Australia several years ago and married her husband earlier this year, was unhappy in her marriage and had considered leaving.

A search on Wednesday of the area around where she left the family car did not provide any clues as to her whereabouts.

She was known to be carrying a large amount of cash but left her passport, phone and other belongings behind along with her two children, aged one and three.

Her family in Germany has been contacted.

can contact Lifeline on 13 11 14;

Suicide Call Back Service 1300 659 467;

MensLine Australia 1300 78 99 78.

AAP