Klopp was sent to the stands during Dortmund's 2-1 opening defeat at Napoli following an ugly confrontation with the fourth official.
He was therefore forced to watch on from the stands on Tuesday as his side beat Marseille 3-0, but UEFA's control and disciplinary body have decided he must spend an extra match away from the touchline.
"Klopp was dismissed from the touchline for behaving in an irresponsible manner towards the fourth official during the UEFA Champions League Group F match against Napoli in Italy on 18 September," a UEFA statement read.
"As the Dortmund coach was not on the bench for Tuesday's game versus Marseille, he has one remaining fixture of his suspension to serve - the encounter with Arsenal FC in London on 22 October."
Dortmund are are considering whether to appeal against the decision, even though they did not appear to miss their coach on Tuesday.
Despite enjoying a better view of the game, Klopp said he preferred to be on the touchline.
"You do see better, but it was uncomfortable," he said.
"It's not something I need very often. I was able to see the team in a relaxed manner from up high, or as relaxing as it can be.
"When the team plays well, it's easier to take, but I've told the lads not to get used to it."
Dortmund are third in the group behind leaders Arsenal, who have won both their opening matches.