Klopp will be missing from the touchline when last year's finalists take on the Gunners at the Emirates on October 22 after being handed an extended suspension by UEFA.
The German coach was sent to the stands for verbally abusing the fourth official in the 2-1 defeat by Napoli last month.
Klopp blew his top when Napoli scored after the fourth official refused to allow defender Neven Subotic back onto the pitch quickly following treatment for an injury.
The 46-year-old served a one-match ban during the 3-0 victory over Marseille on Tuesday but UEFA's disciplinary committee have now doubled the suspension as part of a drive to encourage greater respect for match officials.
"This decision can be appealed. Borussia Dortmund are currently considering whether to go down that route," said the club, who have three days to lodge any protest.
Klopp, whose team have three points in Group F, the same as Napoli, with Arsenal top on six, has repeatedly apologised for his behaviour.
"I made myself look like a monkey out there and that's not on," Klopp told German TV. "I overstepped the mark and it was really pathetic of me."