The Bayern Munich transfer target will undergo surgery in the coming week. There is no timetable for the 23-year-old Germany international's return.
Sane came off for Gabriel Jesus in the first half of City's win following an innocuous incident in which he appeared to get his studs stuck in the Wembley pitch.
The Schalke academy product's impending spell on the sidelines should all but nix a potential return to the top flight of German football.
Bayern have been aggressive in their efforts to recruit Sane to the Allianz Arena. Manager Niko Kovac admitted talks between the parties were underway. "I'm confident and assume that we will get him," Kovac said days before calling City boss Pep Guardiola to apologize for his public statements of interest.