Brown sustained the knee injury in the FA Cup draw with Middlesbrough on Sunday.
Manager Martin O’Neill said: “We don’t think he needs the operation, but he will be two weeks in a brace, two weeks elsewhere and you are looking at probably about eight weeks before he is back.
“But at one stage, it looked like a season-ending injury.”
O’Neill has also revealed midfielder David Vaughan could be missing for several weeks after sustaining ankle ligaments problem during the same game.
O’Neill said: “David was feeling better today, but he is still very, very sore and the swelling is still up, and we are looking at a few weeks for him.”
