Stam, 29, missed last week's 3-1 defeat at Stockport County after suffering the injury during training.
Scans have confirmed Stam suffered a small ligament tear which will require a period of rest.
"The lay-off could be as much as six weeks or as little as three - we don't know fully yet," head physio Marc Czuczman told the club's official website.
The Latics will now be without three defenders - Stam, Sean Gregan (suspended) and Neal Eardley (international duty) - for Sunday's visit of Hereford United.