The league leader in rushing last year, Cornish suffered the injury when he was hit hard by Montreal Alouettes linebacker Kyries Hebert in the first week of the season.
The 29-year-old from New Westminster, B.C., was knocked out but did walk off the field on his own.
He will be eligible to return Sept. 6 when the Stamps play in Edmonton although the team has the right to activate him prior to that date if the situation allows.
Despite Cornish's absence, the Stampeders are 3-0 this season.
The teams says they want to ensure Cornish doesn't return to the field prematurely.
"Jon continues to make progress in his recovery but we understand the importance of being extremely careful with this type of injury and we want to make sure Jon has all the time he needs to get completely healthy," Stampeders general manager and head coach John Hufnagel said in a statement. "We look forward to having Jon back in the lineup and, in the meantime, other players have stepped up in his absence. I’m confident that will continue to be the case."
Cornish was the league's Most Outstanding Player last season.