The on-loan Manchester United player injured his ankle just minutes into his Blues debut against Derby County last weekend and was stretchered off the field.
"Tom has had an early scan which has shown significant damage to the ankle," said Clark.
"There is still quite a lot of swelling there so we can’t put a definite time scale on it, but we can say it will be a minimum of four weeks so that will rule out all of February.
"Potentially it could be longer but we’re waiting to hear more news from Manchester United who are continually assessing him.
"We can’t cancel the loan because we have a contract and obligation to Manchester United, but we’re hoping the lad can make a speedy recovery because we’d like to keep him if at all possible."
Clark continued: "I really feel for him. He’d really impressed us both as a lad and a player in the short time on the training ground. I thought he started the Derby game extremely well when you bear in mind it was his first start in the first team and he was looking very accomplished.
"For that injury to happen ten minutes into your debut he was naturally devastated and we were gutted for him more than anything else. We are hoping fingers crossed that we can get the lad back."