The 35-year-old, who was returning from a fancy dress party and was dressed as a bride wearing a full white wedding dress and veil, was walking through the car park at Bridge Street, near Norfolk Street, Gorbals, when she was attacked.
The woman, who also suffered cuts and bruises during the attack, managed to make her way to the road where she stopped a passing taxi.
Two members of the public also came to her aid.
The attack happened at 2.30am yesterday.
The attacker, who was described as white, Scottish, with dark hair and wearing dark clothing, ran off towards Eglinton Street.
Detective Inspector Liz McLean said: "The lady had been at a fancy dress party nearby and was near the bank at Norfolk Street when she was approached by the man, pulled into the bushes and attacked.
"From CCTV, another couple, a man and woman both wearing fancy dress, are seen in the car park at the time of the attack.
"I would appeal to them to contact us as they might have seen something that could help us with our inquiries.
"I would ask that anyone with information contact police on the non emergency number 101 or Crimestoppers on 0800 555111, where details can be given in confidence."