Monk didn't appeal the charge, admitting to using abusive language towards the officials in the 65th minute of the game at Griffin Park on Tuesday.
He was consequently given the standard penalty of a one-match ban.
The ban takes place with immediate effect, meaning the Blues boss will have to sit in the stands for the visit of Rotherham to St Andrew's on Saturday.
Birmingham currently sit 18th in the Championship after just one win from their first 11 matches.
Norwich, meanwhile, are fifth after going unbeaten in eight games in all competitions.