The 24-year-old was subjected to the terrifying ordeal in Dixon Avenue, Govanhill, in the early hours of the morning.
Detectives said the woman was attacked in the street and a major police operation is now under way.
Several roads around the crime scene, including Dixon Avenue and Cathcart Road, were closed off.
Uniformed officers stood guard at the police cordon as detectives carried out investigations.
The horrific attack comes just a week after police launched a hunt for three men who gang raped a woman.
It also took place in Glasgow’s South Side – around a mile from Govanhill.
Officers are not linking the incidents.
Detectives, who are now conducting a huge CCTV trawl, appealed for help to track down the rapist.
They want to hear from witnesses who may have seen the victim – or her attacker – in the Govanhill area this morning.
There is currently no description of the suspect available.
A spokeswoman said: “We can confirm Police Scotland detectives are investigating a report of a serious sexual assault in the area of Dixon Avenue, Glasgow in the early hours of Monday morning.
“Extensive inquiries are ongoing.”
It comes a week after police appealed for witnesses after three men raped a woman in Toryglen.
The 33-year-old was dragged into a close and raped in Edinbeg Avenue, between midnight and 3am last Saturday.
Anyone with any information is asked to call Police Scotland on 101.