However, manager Chris Hutchings hopes the 33-year-old will be in contention at the weekend.
"We didn't want to risk him (against Millwall). We think three or four days' rest will help the injury and it should settle down pretty quickly," Hutchings told the Birmingham Mail.
"We didn't want to risk playing him at Millwall and possibly losing him for three or four weeks, especially with games coming thick and fast. Hopefully he'll be back in training on Wednesday or Thursday."