The 19 year old was knocked unconscious in an aerial challenge with Real defender Nuri Sahin during Celtic's 2-0 loss on Saturday before being taken to hospital in a neck brace.
"He is coming back with us which is great news," Hoops boss Neil 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."