The 18-year-old was walking through Cardonald Cemetery at about 15:30 on Friday when she was attacked.
Police have said she was touched inappropriately by a man who approached her from behind.
She managed to push him away and he ran off towards Corkerhill Road. The woman was not injured and did not require medical treatment but is said to have been very distressed by the experience.
The suspect is described as white, between 40 and 50 years of age, slim and of gaunt appearance. He had a Glasgow accent.
He was wearing a navy and blue waterproof jacket, black shorts and trainers which may also have been dark in colour.
Det Con Lauren Docherty said: "The young woman... had taken a shortcut through the cemetery.
"She had come in to the grounds from the Mosspark side and was nearing the exit at Tarfside Gardens when the man came up to her and indecently assaulted her.
"He then grabbed her roughly but she managed to push him off and he ran off towards Corkerhill Road.
Ms Docherty added: "The cemetery is used by a lot of local people as a shortcut between Mosspark and the Tarfside flats and I am sure at this time of day there would have been people about who may have seen this happen.
"It was also quite cold yesterday, so if you saw someone wearing shorts - the man didn't look like he was going to or coming from a sports centre - it may have looked out of place."
Anyone with information has been asked to call police on the 101 number or Crimestoppers on 0800 555 111.
A young woman has been indecently assaulted in a Glasgow cemetery.