Hoops manager Neil Lennon confirmed that Brown went under the knife during the international break, but he should be fit to return before the end of the season.
Lennon also revealed defender Thomas Rogne faces a spell out of action with a hamstring injury, while winger James Forrest is not yet ready to return as he continues to have treatment on a back ailment.
The Celtic boss said: "Scott Brown had surgery in the break and so he is looking at a month, four to six weeks.
"Thomas Rogne has a hamstring strain and he will out for two to three weeks, and James Forrest is continuing his rehab at the minute.
"Joe Ledley didn't train due to a slight groin strain but will hopefully train on Saturday and Adam Matthews (hamstring) will train on Monday.
"Charlie Mulgrew is fine, he had a tight hamstring before the Serbia game and Gordon Strachan didn't take any chances with him obviously, but he came through training okay."