The woman was attacked in the early hours of Sunday at Bar 38 on Peter Street.
Police say she was out with friends when a man followed her downstairs to the toilets at about 0100 GMT.
The rapist is described as black, stocky, aged 35 to 38, about 6ft (1.83m) tall, with a shaved head and dent marks in his left cheek.
Witness appeal
According to police, a person banged on the toilet door and asked whether the woman was alright.
This disturbed her attacker, who was wearing a grey shiny jumper with ribbing on the shoulders, and he then left.
Craig Mayberry, from Greater Manchester Police, said: "The woman was simply enjoying a night out with friends when she was attacked.
"We are working closely with the owners of the bar and I'd ask anyone who was there on Saturday night and who remembers seeing the man to contact us.
"We're particularly interested in speaking with the person or people who disturbed the offender and would also ask them to come forward."
The rapist is said to have a Manchester accent and smelt strongly of alcohol and cigar smoke.
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