Klopp, who has already sat out one game when he watched from the stands on Tuesday as his team crushed Olympique Marseille 3-0 in the Champions League, will now also be in the tribune for their Group F game at Arsenal on October 22.
The German coach was sent off in Naples two weeks ago after angrily confronting the fourth official for not letting his defender Neven Subotic back on to the pitch quickly after an injury break, allowing Napoli to score in the meantime.
"This decision can be appealed. Borussia Dortmund are currently considering whether to go down that route," Dortmund said in a statement.
Klopp, whose team have three points in Group F, the same as Napoli, with Arsenal top on six, has repeatedly apologised for his behaviour.