The midfielder has been struggling with the injury all season and has only been playing intermittently, usually in the big games.
Brown started the UEFA Champions League match against Benfica at the Stadium of Light but was replaced by Kris Commons in the 64th minute, shortly before Ezequiel Garay's strike secured the hosts a 2-1 victory.
Celtic boss Neil Lennon said: "Scott Brown has run his course, we may have to book him in for surgery. We are looking at eight to 10 weeks.
"He has been pushing himself to the limit and we can't keep asking him to put himself through the amount of distress that obviously he was doing towards the end of his time on the pitch.
"He has been a huge player for us this season, I think it is time to get the problem addressed and hopefully he will have something to look forward to in the new year."