A woman has been stabbed in the face during an apparent domestic violence incident at an Adelaide shopping centre, police say.

Key points: The woman was taken to the Royal Adelaide Hospital with non-life-threatening injuries

The woman was taken to the Royal Adelaide Hospital with non-life-threatening injuries Police said the suspect fled the scene

Police said the suspect fled the scene A 26-year-old man was arrested at a nearby train station

Police said a man had been arrested following an incident at the Elizabeth Shopping Centre that happened about 7:30am.

Officers were called to the shopping centre, in Adelaide's north, after receiving reports that a woman had been stabbed during a "domestic disturbance".

Police said they found a 29-year-old woman with a stab wound to her face.

She was taken to the Royal Adelaide Hospital with non-life-threatening injuries.

Police said the suspect fled the scene.

A search was conducted in the area by Northern District police who located the suspect at a nearby train station.

Police said the 26-year-old man from Salisbury North was expected to be charged with aggravated assault causing harm.