An 18-year-old woman has been arrested and charged over an alleged stabbing murder at a home at Kilburn in Adelaide's inner north.

A 61-year-old woman was treated by ambulance crews but died at the scene on Goodman Avenue, where emergency services were called just after 5:10pm on Friday.

The woman had been stabbed multiple times and police are currently searching the area for the weapon.

"At this stage it's unclear what the weapon is, but we would suspect that it is a knife and at the moment we are in the area with the assistance of SES [State Emergency Service] volunteers," Detective Inspector Billy Thompson said.

An 18-year-old woman was arrested by the Major Crime Investigation Branch about 11:00pm and charged with murder.

The suspect is a "resident of the same suburb" but police said they could not be more specific, given the matter was now before the courts.

Police are investigating links between the two women, and the incident is not believed to have been random.

"We do believe that they may have been known to each other, that's yet to be categorically confirmed," Inspector Thompson said.

"We believe that the accused person may have been at the address before, I don't want to go into reasons why that would have been at this stage.

"We're confident there is no-one else involved in this incident."

Police and SES personnel are searching the area for the weapon. ( ABC News: Carl Saville )

The victim had lived in the area with her husband for "quite some time" and was well known in the local community, police said.

"We are particularly interested in the movements of anyone in the Goodman Avenue area between 3:00pm and 5:00pm," Inspector Thompson said.

"We've already spoken to quite a number of people in the area.

"We're particularly interested in anyone who may have CCTV in the area or anyone who may have dashcam footage in the area in that particular timeframe."

The alleged killer has been refused bail and is expected to face the Adelaide Magistrates Court on Monday.

Police have asked anyone with information to contact Crime Stoppers on 1800 333 000.