And the Dortmund coach could yet see the sanction extended, with UEFA due to discuss his punishment further next month.
Klopp was sent to the stands in Dortmund's opening Group F meeting with the Italian side after reacting angrily to the decision not to let Nevan Subotic return to the pitch in the build-up to Gonzalo Higuain's opening goal.
The German side ultimately fell to a 2-1 defeat, with the coach apologising during his post-match press conference for his outburst.
"I have to take the blame, that was just dumb," he said.
However, despite his apology, he has been handed a punishment by UEFA and will now miss the clash against Marseille on 1 October.
And a UEFA spokeswoman confirmed that there could yet be further action to follow.
She was quoted as saying by ESPN: "A decision about a possible extension of the ban will be made by the control and disciplinary chamber on October 2."