The 21-year-old has returned to parent club Manchester United for treatment having lasted just 15 minutes of his Blues bow in the 3-3 draw against Derby before leaving the field on a stretcher.
Thorpe arrived at St Andrew's on transfer deadline day on a deal until the end of the season and boss Clark has not given up hope of seeing him play again this term, although he knows the centre-back faces at least an immediate spell on the sidelines.
"Tom has had an early scan which has shown significant damage to the ankle," Clark told the club's official website.
"There is still quite a lot of swelling there so we can't put a definite timescale 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 added: "For that injury to happen 10 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."