The victim was attacked behind Didsbury library in the early hours of Saturday, at around 1.25am. The area around the library, including a walkway which links Wilmslow Road to Barlow Moor Road, was cordoned off by officers yesterday.
The offender is described as white, of medium build, in his late 40s, clean shaven and bald or with a shaved head.
Police are appealing for information from members of the public and were keen to reassure residents in the area. Det Insp Mark Radford said: "I understand this incident has caused a lot of speculation and unrest in the community, and that is why it is important we issue this appeal.
"I want to stress that we are investigating this matter thoroughly and officers will do everything they can to establish the circumstances surrounding exactly what happened and this is where the public can help us.
"If you saw or heard anything near Didsbury library, or recognise the man from the description, then please come forward as what you know could be vital.
"Specially-trained officers are also providing support to the woman."
Anyone with information should call Didsbury CID on 0161 856 6152 or Crimestoppers, anonymously, on 0800 555 111. Tweet