The 51-year-old was assaulted as she made her way to work yesterday at about 5.45am.
Her ordeal began as she walked through the Green Park area of Glasgow Green. The man approached her and assaulted her, before she managed to run away.
She did not need hospital treatment, but police said the woman had been left "shaken" by the attack.
About a dozen forensic officers wearing protective white suits were seen carrying out extensive investigations at the scene.
A forensic tent was erected and officers carried out a fingertip search of the area.
Detectives cordoned off a large area of Green Park. A mobile police office, as well as two police vans, remained at the scene. Uniformed officers also stood guard.
No description of the attacker is yet available, but police have asked anyone who was in the area at that time to contact them.
A police spokeswoman said: "Inquiries are continuing."
Anyone with any information is asked to call 101 or Crimestoppers on 0800 555111.