A 25-year-old woman remains in a critical condition at the Royal Adelaide Hospital after allegedly being seriously assaulted by a man late last month.

Police are investigating this incident after the woman was admitted to the Alice Springs Hospital with an eye injury by family around 5am on Tuesday.  She was transferred to Adelaide later on the same day.

It is alleged the woman had been assaulted by a man known to her, in Larapinta some days prior to seeking medical help.

Investigations into the incident continue.