The horrific attack happened as the 22-year-old was walking along Mosspark Drive, close to Cardonald Library, at around 12.10am yesterday(SUN).
It is understood the young victim was pounced on as she made her way home on the South Side of the city.
There is no description of the suspect available.
Police today appealed for any witnesses to come forward, in a bid to catch the culprit before he strikes again.
A spokeswoman for Strathclyde Police, said: “We received an allegation of a serious sexual assault on a 22-year-old woman in Cardonald, at around 12.10am on Sunday.”
“Our inquiries are ongoing.”
The library, which is run by Glasgow City Council’s arms-length organisation Glasgow Life, opened as normal earlier today(MON).
Anyone with any information is asked to contact Strathclyde Police on 0141 532 2000.