The club made the announcement via their Twitter account Friday afternoon, but declined to elaborate on the extent of the injuries.
The most outstanding player in 2013 missed six games earlier this year with a concussion. Cornish suffered the injury in the first game of the season against Montreal.
Cornish has been on a tear since returning to the lineup, posting three consecutive 100-yard games, including scoring a pair of touchdowns and compiling 209 all-purpose yards in Calgary's 40-33 come from behind win over Toronto last week.
It's a big loss for Calgary (10-1) who hold the the top spot in the CFL standings.
Cornish's rest comes at a good time for the Stampeders though, who are approaching the season's home stretch.
Following their visit this Sunday to Montreal, Calgary will face both B.C. (7-4) and Saskatchewan (8-3) twice over their remaining six games. Both the Lions and Roughriders are eager to pull closer to the Stamps in the standings, and solidify their playoff positions.
Allowing Cornish the weekend off against Montreal (3-8) will hopefully give the running back the necessary time to get back to full health prior to Calgary's playoff push.