The man was arrested at the scene early this morning and was expected to appear in Adelaide Magistrates Court today.

No motive has been established for the killing at the Colonnades Shopping Centre at Noarlunga.

SA Police said officers and paramedics responded to reports of a woman with serious head injuries at the shopping centre just before 12.15am this morning.

“Police and paramedics provided first aid, but sadly the 36-year-old Ethelton woman was pronounced dead at the scene,” police said in a statement.

A 20-year-old man of no fixed address was arrested at the scene and has since been charged with murder.

“While the investigation is in its early stages, police have not been able to establish any links between the suspect and the victim,” police said.

– with AAP