Clark's condition becomes aggravated when playing at higher elevations, WPXI-TV, Pittsburgh, reported Wednesday.
"Looking at data and all the variables he is at more risk, so we're not going to play him," Tomlin said. "It's just that simple."
WPXI-TV said Clark's teammates urged the Steelers' leading tackler to sit out the game, arguing the game isn't more important than his life.
Backup Ryan Mundy, who has had two career starts, will take Clark's place in the starting lineup for the wildcard game.