The Frenchman was originally handed a two-match suspension after being caught relaying messages by telephone from his seat in the stands to the technical area as he was already serving a ban carried over from last season.
"The UEFA Appeals Body has rejected the appeal lodged by Arsenal FC and Arsene Wenger against the two-match suspension handed to the manager in the wake of the English club's UEFA Champions League play-off first leg against Udinese Calcio on 16 August," said a statement from UEFA.
"Wenger will now be suspended from carrying out his duties at Arsenal's next two UEFA competition matches - the UEFA Champions League group stage games against Borussia Dortmund and Olympiacos FC on 13 and 28 September - in accordance with the decision taken by the UEFA Control and Disciplinary Body on August 22.
"The manager was awarded this suspension for not abiding by an earlier decision of the Control and Disciplinary Body during the Udinese home game - in which Wenger was serving a one-match ban imposed following Arsenal's final UEFA Champions League game of last season.
"The control and disciplinary body also fined Arsenal 10,000 euros for improper conduct by their officials during the match against the Italian team in north London."