The 86-year-old woman was found by family members within her home on Kirkhill Drive at around 9.30pm on Friday, May 28.
She was taken to Ninewells Hospital by the Scottish Ambulance Service for treatment where she remains in a stable condition.
Enquires to establish the circumstances of the incident and how the woman was injured remain ongoing.
Officers are appealing to anyone who may have seen anything suspicious in the area to come forward.
Detective Inspector Marc Lorente from the Specialist Crime Division said: “At this stage it is still unclear how the woman became injured.
“We are keen to talk to anyone who was in the area between Wednesday, 26 May and Friday, 28 May, and saw anything out with the ordinary to contact us as soon as possible."
Anyone with information can contact the police on 101, quoting incident number 2847.