The 30-year-old Republic of Ireland international recently returned to the Blues squad following compassionate leave.
"It's an absolute nightmare," Clark told Birmingham's official website. "We got really concerned as he had a lot of bleeding in his groin area which came out in a bruise.
"When we had it scanned, the hip area was the problem so he is certainly out for the six games. Keith Fahey has shown in the last two away games what an outstanding midfield player he is.
"It was no coincidence that we put in two tremendous appearances away from home. We weren't conceding and we were playing good football with him in the team."
Birmingham host Millwall in the Championship on Saturday afternoon.