At about 7.50pm, police were called to a house in Goodman Avenue after reports that a woman had been assaulted by a man.
The victim was taken to the Royal Adelaide Hospital in a serious condition.
Police believe the victim and suspect are known to each other, and the incident was not random.
The suspect is described as about 180cm tall, slim build, short crew-cut hair and was wearing a light-coloured tank top, black shorts and white shoes.
Anyone with information that can assist police is asked to call Crime Stoppers on 1800 333 000, or online at https://sa.crimestoppers.com.au