Clinton-Dix, who has racked up 24 tackles this season for the top-ranked Crimson Tide, is off the team until further notice, the coach said.
Saban wouldn't divulge any details about what the third-year junior had done.
"When guys get suspended, I never, ever say what it's for, all right? So I'm not going there, so don't ask me," he said. "It's the way it always happens. Every guy, if they do right they wouldn't be getting suspended."
Clinton-Dix is considered one of the best safeties in the nation and is a projected first-round draft choice.
He was the Tide's interceptions leader with five last season.