Carr was forced to undergo srugery after his knee began to swell up in training earlier this week.
"Monday and Tuesday he was training really well prior to the Peterborough United game and we had pencilled him in to play, and he was really positive," Birmingham boss Lee Clark told the Birmingham Mail.
"Prior to the game he felt a little problem in the knee so we ruled him out.
"And over the course of the next few days it became really swollen, so we got him down to London for an appointment with the specialist who worked with him last season who went inside the knee and found quite a bit of damage.
"It's a bit more of the cartilage and other parts of the knee because obviously the more times you go and operate the weaker it becomes.
"It's horrific news. It's huge blow for the club, but more importantly for the lad himself. He's going to be out for a minimum of six months."