The 30-year-old picked up the problem in Saturday's 1-1 draw with Mansfield Town.
Plymouth physiotherapist Paul Atkinson told the club's official website: "He has fractured and dislocated his finger and early indications are that it is going to be a lengthy lay-off.
"It's obviously worse for him because he is a goalkeeper. If he was an outfield player, we might be able to strap up the injury and he would be able to carry on playing.
"The consultant has asked a colleague, who is the specialist on hand injuries in the South West, for his opinion. Luke will be seeing him on Wednesday. After that, we will be in a better position to give a more precise time-frame for treatment and recovery."
McCormick's injury means that Jake Cole, who has kept two clean sheets in 10 first-team appearances this season, will be between the sticks when the Pilgrims travel to Northampton Town this weekend.