The 23-year-old will remain at the City Ground to receive treatment on the injury.
The Reds insist the problem is not serious and Perch is expected to resume training when the rest of the squad return from the Algarve.
Long-term injury victim Julian Bennett will also miss out. The left-back has been sidelined since Boxing Day with a knee ligament injury and is continuing his rehabilitation.
"There are one or two guys that we feel would benefit more from staying in Nottingham," Forest manager Billy Davies told the club's official website.