The 27-year-old sustained the damage in the early stages of the Blues' pre-season campaign and has already undergone surgery.
Birmingham announced on their official website that they will have a clearer picture of the midfielder's rehabilitation process in the coming days.
Davis, who has made 167 appearances since joining City from Wolverhampton Wanderers in August 2014, now hopes to return stronger later this year.
"Op successful! Ill be back stronger than ever thanks for the messages of support means a lot," he posted on his personal Twitter account.
Op successful! Ill be back stronger than ever 💪🏽😡thanks for the messages of support means alot #kro— David Davis (@Diggad1991) July 4, 2018
Davis was used in 38 of Birmingham's league matches last season, starting 33 of those.