The 26-year-old German suffered the injury in the 1-1 Premier League draw with West Brom and was taken off on a stretcher after 56 minutes.
Kirchhoff, who can also play at centre-back, missed the start of the season with a similar injury before returning at the start of September.
Sunderland are bottom of the table after two points from seven games.
It is the latest injury setback for the Black Cats after winger Adnan Januzaj was ruled out for a minimum of six weeks with an ankle injury.
Sunderland midfielder Jan Kirchhoff has been ruled out for six to eight weeks with a hamstring injury.