The woman was walking past Grafton Street, just off Clark Way, when the man allegedly struck.
GMP said she was being supported by specialist officers.
The force said it was keen on identifying anyone who was in the area around Clark Way, Grafton Street, King Street, the footbridge and the nearby bus station around the time of the assault.
Det Ch Insp Abdul Kahar said officers were doing everything possible to provide appropriate care to the woman.
“This is a truly horrific crime and we are determined to bring the person responsible to justice,” he said.
“No woman should feel unsafe when walking the streets of Greater Manchester, and we are committed to doing everything we possibly can to progress this investigation at pace.”
He urged anyone who may have seen anything suspicious in the area at the time to get in touch.
