The 26-year-old had been running along the Bergisel mountain when she suddenly fell and plunged off the side on Friday, police spokesman Ernst Kranebitter said.
Two students discovered the severely injured woman near the Drachenfelsen (Dragon rock) panorama platform overlooking the steep ravine of the Sill river.
Shortly after hitting the ground, Kadic managed to call her brother and inform him of the accident before losing consciousness, Kranebitter said.
She was rescued by helicopter and taken to a hospital in the city of Innsbruck, where she has not yet regained consciousness.
The exact circumstances surrounding the accident remain unclear, but police said the 2013 beauty competition winner was an avid runner who knew the area well.