Klopp, who was sent to the stands for verbally abusing the fourth official in the 2-1 defeat by Napoli last month, sat out a one-match ban for the 3-0 victory over Marseille on Tuesday.
But on Thursday, UEFA's disciplinary committee announced it had doubled the ban as part of a drive to encourage greater respect for match officials.
The explosive 46-year-old coach later apologised for his outburst and admitted on German TV: "I made myself look like a monkey out there and that's not on. I overstepped the mark and it was really pathetic of me."
Borussia have three days in which to lodge an appeal.
Jurgen Klopp touchline ban extended to Arsenal clash
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