The Blues captain went under the surgeon's knife in London on Wednesday.
Clark admitted this latest set-back for the 36-year-old former Ireland international was a "massive blow" for both the player and the club.
"Stephen Carr had surgery on Wednesday for a knee problem and will be out for a minimum of six months," said the Blues boss.
"It's a huge blow for the club but more importantly for the lad himself because he is the leader both on and off the field with how he performs and goes about his business.
"He worked massively hard over the close season and in pre-season was absolutely flying. He tweaked the thigh muscle against Antwerp and as he was rehabbing from that he felt a little problem in the knee and over the course of the next few days it became really swollen, so we knew there was a problem.
“We got him down to London for an appointment with the specialist who worked with him last season and when he had a look inside the knee he found quite a bit of damage."
Despite the player’s long-term absence Clark feels that his desire to continue playing will see him put all his efforts into his rehabilitation.
"I know his desire and determination and I know that whatever rehab programme he’s given he’ll do it to the letter and he’ll do every single day, whether he’s in the club being supervised by the staff or whether he’s on his own," he said.
“He’s got a great determination and he’s got a great attitude and desire to carry on playing. He’s still super-fit, which gives him a great chance, so if there’s any way of him getting back before the targets that I’ve set or when the target is set it will happen because you know he will do everything that’s being asked of him."
Clark also confirmed that in Carr's absence Steve Caldwell will take the captaincy role out on the pitch.
"Steven Caldwell takes over as long as he is in the team, because he's next in line," added Clark. "But Stephen Carr is still a very important member of the football club and the squad and he just carries on those duties as normal. He’s got his rehab to concentrate on but that doesn’t change anything, because it’s still an important job and Stephen is still a very well-respected member of the group."