The 37-year-old was sent to the stands during the closing minutes of the 1-0 defeat at Ashton Gate on 27 September.
He admitted a Football Association misconduct charge of "using abusive and/or insulting words towards a match official".
Monk will serve his ban in Saturday's Championship match at Derby.
Leeds United boss Garry Monk has been given a one-match touchline ban and a £2,000 fine for using abusive language in the loss to Bristol City last month.