Officers are appealing for anyone with any information to come forward after the 35-year-old victim, who was dressed as a bride wearing a full white wedding dress and veil, was attacked as she walked through the car park at Bridge Street, near Norfolk Street in Gorbals.
The woman, who suffered cuts and bruises during the late-night 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 after the attack, which happened at 2.30am on Sunday.
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: "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."