The centre-back was replaced by Jonathan Spector just before half-time against The Robins and is a doubt for Saturday's trip to Blackburn.
When Spector joined the action he took up the right-back position, with Paul Robinson moving to centre back alongside Stephen Caldwell.
"Curtis has had an ongoing ankle problem and he jarred it against Bristol," said Blues boss Clark.
"He wanted to carry on but I think there was one incident where then ball has gone over the top and he tried to run and he wasn’t running freely. So it was my decision really.
"I didn’t want him to inflame it even more and for him to be out for an even longer period. He’s obviously a doubt for the weekend but he showed his desire and commitment because he didn’t make any indication about coming off, it was just what I’d seen and I took it out of his hands."
If Davies is not fit for Saturday's trip to Ewood Park, Pablo Ibanez is likely to come back into the reckoning. The Spaniard has been out for several weeks with a broken bone in his foot, but he is back in playing action on Wednesday afternoon for the Blues development squad against Sheffield Wednesday.