Cornish left Saturday's 18-13 loss to Winnipeg in the second quarter after bouncing his head off the McMahon Stadium turf. The CFL's leading rusher did not return to the game.
Price was tackled hard on the final play of the game.
The Stampeders did not identify the players' injuries in a statement issued Monday, but said both players are "progressing well" and are expected to play in the West Division final Nov. 23 at McMahon.
Neither player will travel with the Stampeders (14-3) to Vancouver, the football club said.
Cornish, the CFL's Most Outstanding Player in 2013, leads the league in rushing with 1,082 yards even though he's appeared in just nine games this season.
Cornish sat out six games in July and August with concussion symptoms. He took a high hit from Montreal's Kyries Hebert in the season-opener. Cornish, who turns 30 on Wednesday, also missed two other games because of injuries.
Price has 34 catches for 544 yards and a pair of touchdowns this season.