Woman found dead in Adelaide's CBD sparks murder investigation

A murder investigation been launched into the death of a woman who was found stabbed to death inside a home in Adelaide's CBD.

Major Crime detectives believe the victim was killed several days ago.

Police discovered the woman's body in a bedroom around 6pm last night.

Sturt Street was quickly shut down as Major Crime detectives began examining the crime scene - an historic two storey home.

Detective Superintendent Des Bray says the 39-year-old victim, who was stabbed, had been reported missing on Sunday.

"The last confirmed sighting of her was on 11:30pm on Thursday night," Superintendent Bray said.

"During the time until the Sunday, friends became concerned (and) she failed to attend her work, she works in a restaurant at the airport."

Police believe the victim's silver BMW was stolen by the offender. It was found earlier today behind a pizza restaurant on West Terrace.

A large section of Sturt Street has been blocked off this morning as investigators hunt for a possible murder weapon.

Police say the victim was a boarder at the home, which is owned by two prominent public servants, who investigators say are not suspects.

Anyone with information is being urged to contact Crime Stoppers on 1800 333 000.