The 32-year-old Serbian striker, who has scored six goals in 22 appearances this season, was set to start Saturday's game at St Andrew's.
But a disgusted Clark says he has now changed his plans as a result of what he witnessed during Thursday's training session.
"He (Zigic) won't be involved," said Clark on Sky Sports News. "I witnessed possibly the worst training session, in terms of a professional footballer, I've ever come across yesterday.
"We'd done our preparation work for Watford and he was in the team and I was disgusted when I walked off.
"He was starting in the team and he knew that because we had done our preparation on Thursday about how we were going to approach the game, both with and without the ball.
"He is a very well paid guy and you've got to earn that and what he dished up yesterday was what, since I left school at 16 and have been in professional football, not technically or tactically, the worst training session I have ever seen."
Clark revealed that this is not the first time Zigic, who has not started a game since 29 December, has been unsatisfactory in training with the Blues.
"This has been coming," he said. "Whether he is angry because he has not started enough games in recent weeks, that could be valid. But does that mean he can down tools and not try? The fans and the football club deserve more than that."
When asked about Zigic's future at the club, Clark replied: "That is up to Nikola. I haven't had a bust up with him. There has been no shouting match. It is up to him."
Serbia international Zigic joined Birmingham from Valencia in May 2010 and has scored 26 goals in 99 games for the club.