The suspension was imposed by European football's governing body on top of the one-match ban he received for a straight red card for a foul on Barcelona's Neymar.
Having already missed the Group H fixture at home to Ajax, Brown will also be unavailable for the return match in Amsterdam on Wednesday, and the showdown with Milan at Celtic Park on November 26.
On the decision, manager Neil Lennon said: "It's been turned down, we didn't win the appeal.
"It's disappointing. We felt we had a good case. I feel the ban is excessive for a misdemeanour, or whatever you want to call it.
"It's a blow for us and for Scott but we will just have to deal with it.
"You are hoping to have the ban reduced but if not, you have contingency plans just in case. We do have an idea of who will play there on Wednesday.
"We will have to keep an eye on Beram Kayal, we can't afford to lose too many players in that area because it's a crucial part of the pitch."
Brown conceded in the aftermath of the incident that he had made a mistake but was adamant the decision was harsh.
Celtic sit third in Group H with three points from as many games.
