Rodgers suffered the concussion after being hit late in overtime in Sunday's 16-13 loss at the Washington Redskins.
New NFL regulations on concussion mean Rodgers will have to go through an independent doctor's visit and his recovery may not be in time for the Dolphins game.
"It's definitely possible (he will be out). I know at a minimum he will miss some practice time," McCarthy told reporters.
McCarthy said tight end Jermichael Finley would have surgery Tuesday on his knee injury although he expressed hope that the player might be able to feature again this year.
Safety Derrick Martin has a knee sprain and McCarthy said: "It will likely be more than a couple of weeks with Derrick."
The packers are 3-2 in the NFC North behind the 4-1 Chicago Bears.
(Reporting by Simon Evans in Miami; Editing by Sonia Oxley)