Emergency services were called to the Aberdeen City War Memorial at Schoolhill after the incident in the early hours of Friday.
The 20-year-old had fallen from the granite structure, which dates back to 1925, and seriously injured her head.
Sergeant Eoin Maxwell said: “Officers are making enquiries into an incident which occurred between 2.15am and 2.30am on Friday, where a 20-year-old female sustained a head injury due to an apparent fall at the Aberdeen City War Memorial at Schoolhill in Aberdeen.
“She was subsequently taken to Aberdeen Royal Infirmary.
“Anyone with information about this incident is asked to contact Police Scotland on 101 quoting reference 0406 of April 6.”