According to 'Sky Sports', the break was initially thought to be his wrist, though it turned out to be the lower part of his arm.
The Irish FA announced on Tuesday that the winger had undergone surgery to repair the break after an awkward fall in training.
Ireland play Wales in Cardiff on Thursday night in the UEFA Nations League, though McClean will have to miss the game.
The 29-year-old will also miss a friendly against Poland and up to seven matches for the 'Potters'.