McCarthy suffered a labral tear during the 1-1 draw with QPR a month ago and after failing to respond to treatment, it was decided an operation was necessary.
The 23-year-old had been Reading's first choice goalkeeper since September, edging out Adam Federici in the position.
"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," said McDermott.
Reading may also be missing Pavel Pogrebnyak for Saturday's trip to Southampton after the Russian striker sustained an unspecified injury while playing for the reserves in midweek.
The Royals are four points adrift of safety and are targeting a victory at St Mary's that will see them supplant their fellow relegation strugglers in 18th place.
McDermott insists being involved in thrilling, high-scoring matches - such as Saturday's 4-3 defeat by Manchester United - is not enough.
"We've had some fantastic games at Madejski Stadium with lots of goals which is really entertaining for the fans, but our fans want results as well," McDermott said.
"We're creating things and scoring goals, now we have to get results because that's what we're in the business for.
"It's possible to take satisfaction from matching a team like Manchester United - look at the finances and budgets we're up against. But myself and the players want to win games."