The 18-year-old student was jogging through Jubilee Park about 11.30pm on a lit track between Canongate and Maori Rd when she fell or was tripped by her attacker.
The man assaulted her and attempted to rip off her shorts. When she fought him, he cut her face with a broken bottle. She continued to defend herself and the man ran off towards Maori Rd.
The jogger sustained a deep wound to her forearm, which required stitches, and cuts to her forehead and cheeks. Her palm was also sliced.
Detective Dave Checketts, of Dunedin, said the woman called 111 when her attacker retreated and she was treated at Dunedin Hospital and released, but was still distressed yesterday.
"It was pretty ugly. This was no run-of-the-mill assault."
Running or walking alone at night, especially in an isolated area, was not advisable, Det Checketts said.
Police urged anyone who had seen the female jogger or any other people in the area around Jubilee Park, Canongate or Serpentine Ave area late on Monday to contact them.
The attacker was described as Caucasian, in his mid to late 20s, with shortish dark hair. He was wearing a dark-coloured nylon windbreaker and possibly jeans.