Brown appeal rejected by UEFA
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 and felt the ban was excessive.
"It's a blow for us but Scott will have to deal with it."