Lennon is expecting the 19-year-old to be out of action for up to six weeks.
"He is coming back with us which is great news," Lennon told the club's official website. "He needs a plate inserted in his jaw and I think he may made need an extraction of a tooth which has been damaged.
"Thankfully, there are no neck or head injuries. It was very similar to the injury Henrik [Larsson] had when he broke his jaw against Livingston that day. So we might be looking at four to six weeks.
"Obviously it's a blow but it could have been a lot worse and he's a young lad who will recover quicker than most. He had a stable night in hospital, and thankfully he is coming home with us today."
McGeouch made six SPL appearances last season, scoring one goal.