The former Tranmere man suffered the injury in yesterday night's 2-0 defeat at the hands of Stoke City and was replaced by Drissa Diallo after an hour of play. Drissa then played alongside Georges Santos in the heart of the blues defence in McGreal's absense.
Speaking to the Official Club Website, Town manager Joe Royle confirmed: "Johnny Mac felt the knee in the first-half at Stoke but we hoped it might settle down. It started to become sore though and he had to come off but it's a tweak, not a tear like the injury he sustained twice last season.
"We will have much more of an idea on when he will be back on Friday after the knee has settled down but at the moment, it looks like it might be a week or two.
"He certainly looks very doubtful for Sunday's game but we will take another look at the end of the week and see where we go from there."