The 30-year-old, who is currently on loan at Nottingham Forest, went under the knife in Glasgow a fortnight ago due to an infection that had developed in his mouth.
McCormack has been unable to train for the past three weeks due to a separate Achilles problem, and he has now been advised by medics not to train for between 10 days and a fortnight to help reduce the swelling to his face.
"It's been a freakish couple of weeks in what has been an abnormal season for me," he told the Daily Mail. "Forest have been good with me. I wanted to help them but the doctors have advised that I avoid contact in training and rest up.
"I'm not used to seasons where I don't play a lot of games and get my goals. I desperately want to get back to that. Obviously, the move to Villa didn't start as planned but hopefully I can get myself sorted and come back in the summer nice and fresh."
McCormack is under contract with Villa until 2020, having signed a four-year deal when joining from Fulham last summer.