The influential midfielder, who recently returned from long-term compassionate leave, has a hip/groin injury which requires further medical investigation and treatment.
"It's an absolute nightmare," admitted the Blues boss. "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.”
Fahey proved his undoubted importance to the team in the away victories at Middlesbrough and Crystal Palace, as Clark acknowledges.
"Keith Fahey has shown in the last two away games what an outstanding midfield player he is," he said. "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.
"Obviously with Jonathan (Spector) being out as well in the last couple of games you're just missing that little bit of a more defensive minded player in the middle of the pitch. The lads who do the defensive side go under the radar a little bit, but they have a huge part to play."
The player himself is understandably disappointed that his season has come to a premature end, but Clark says he is philosophical about it.
"Of course he’s very frustrated," added Clark. "But I think because he’s a senior player he understands that injuries are part and parcel of the game and he’s just got to try and push on and we’ve got to get to the root of the problem and get it rectified.
"We’re sending him to a specialist who can hopefully give us the right answers and give us a solution."
Meanwhile, the Blues boss confirmed that he will be without the services of Chris Burke (ankle) for tomorrow's game against Millwall and that American international Jonathan Spector is doubtful.
"Chris hasn't got a chance for tomorrow," he said. "Jon is going to train with us, but he is touch and go."
Marlon King, Stephen Carr, David Murphy and Will Packwood are all long-term injury absentees.