Police say they were in the process of conducting the investigation at an address in Mannahill, South Australia, when a 41-year-old man took his own life at the property.
Officers had conducted a "lengthy record of interview" on Wednesday with Tanja Ebert's husband Michael Burdon, who was not under arrest at the time, Detective Superintendent Des Bray, the officer in charge of the South Australia Police Major Crime Investigation Branch, told reporters at a press conference.
He said they then carried out a forensic search of the family home accompanied by Mr Burdon and other family members.
"During the course of the afternoon, police momentarily lost sight of Michael, and then very shortly after heard a muffled gunshot," he said.
Tanja Ebert with her sons.
No-one else sustained injuries and the man's children are safe with relatives.
A police commissioner's inquiry and coronial investigation have been launched into the full circumstances of the death.
Det Spt Bray says the police have "grave fears" that missing woman Tanja Ebert has been murdered and their investigation is focusing on the remote South Australian home she shared with her family.
The 23-year-old is a German citizen of Caucasian appearance around 165-170cm tall, has a slim build with blue eyes and blonde hair. She has a German accent.
She was last seen on Tuesday August 8.
Last sighting of missing woman Tanja Ebert
The last independent sighting of her was on CCTV footage at the South Australian Museum in Adelaide with her family, at around 3.20pm.
Her husband, whom police say she met and married shortly after she arrived in Australia five years ago, claimed she reportedly got out of her family car at Roseworthy that day and walked away from him, their two young sons, aged one and three, and her personal possessions, including her passport, phone and purse.
A relative called police to report her missing on the morning of Thursday August 10.
A search operation was launched by Major Crime Police, the Barossa Local Service Area, the STAR Group and Mounted Operations, alongside the police helicopter and State Emergency Service (SES) volunteers.
A murder investigation has been launched.
"We have searched this area – near the wheat stacks about 1.5 kilometres north of Roseworthy - and have found no trace of this young woman," said Det Spt Bray.
"I'm asking that anyone who has had recent contact with her to come forward and speak with investigators by calling Crime Stoppers on 1800 333 000.
“We are aware there had been some issues in the marriage; however, at this time, we are keeping an open mind with regard to suspects.
"As with matters of this type, we are making inquiries to rule out the involvement of those who saw her last."
Readers seeking support and information about suicide prevention can contact Lifeline on 13 11 14.
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