The 46-year-old will now have to watch next Tuesday's Group F clash against French runners-up Marseille at Signal Iduna Park from the stands.
Klopp received the ban after verbally abusing the fourth official, who refused to allow defender Neven Subotic to return to play during their fiery encounter against joint Serie A leaders Napoli at the Stadio San Paolo on September 18.
He was subsequently sent to the stands by the match referee and later apologised for his outburst.
UEFA's disciplinary commission will meet on October 2 to decide whether Klopp will be suspended for a further match or handed a fine.
"I made myself look like a monkey out there and that's not on," he told ZDF television following the match.
"I overstepped the mark and it was really pathetic of me.
"I've already apologised to the team, the referee and the fourth official. I got it wrong.
"I have to accept the blame for this red card, it was just stupid of me."