McCarthy underwent an operation in London on Monday after sustaining the problem in the Premier League draw at QPR on November 4.
The Royals had initially hoped that the shot-stopper would soon be back in action after a period of recuperation, but further examinations deemed that it was essential for him to go under the knife.
Reading's head of sports medicine Luke Anthony was reluctant to give a date on his expected recovery, but admitted that they will 'try' to get McCarthy back in action before the end of the season.
Anthony said: "We had an encouraging MRI scan on the Monday after the QPR game, then we saw a shoulder specialist the following day and he was also positive that Alex should be able to recover with a conservative rehab programme.
"But it soon became clear that the structural damage wasn't going to improve without surgery.
"We saw another consulant and, on Monday, Alex successfully had his labrum tissue repaired.
"Understandably supporters will ask how long Alex will be out, and it's difficult to put a time-frame on his return.
"The most important thing is for Alex to make a full recovery and return in optimal condition. If that allows him to return before the end of the season then that is something we will try for."
Royals boss Brian McDermott added: "We don't want to put a time frame on it except to say it will be a long time. A decent amount of time."
The England U21 international started out as deputy to Adam Federici, before taking over as first-choice for Brian McDermott's side in September, making eight appearances before his untimely setback.
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