The official had sent off both Jermaine Beckford and Tresor Kandol during the League One game that ended Leeds' 100% winning start to the season.
At a Regulatory Commission hearing last week, Wise was fined £5k and given a three-match touchline ban that starts on Friday November 9.
An FA spokesman said: "The Commission invoked a previous suspended one match touchline ban and issued a further two match ban.
"In reaching its decision, the Commission took into account Wise's poor recent disciplinary record."
Wise will be missing from the touchline for United's FA Cup 1st-round match at Hereford United on November 9, their JP Trophy tie with Bury four days later and their League One game at home to his former club Swindon Town on November 17.
Meanwhile, The FA have charged referee McDermid with using abusive and/or insulting words towards Wise.
The incident is alleged to have occurred following the match against Gillingham that ended in a 1-1 draw.