Wenger and Nasri were charged with using "inappropriate language" towards referee Massimo Busacca as Arsenal were beaten 3-1 at the Camp Nou. They had been left frustrated by the dismissal of Robin van Persie for kicking the ball away.
Wenger had announced he would deny the charge and called on UEFA to show some "humility", while comparing the organisation to a "dictatorship".
The pair are now set to miss Arsenal's next European game in the Champions League or Europa League, although they will be able to appeal the decision.
UEFA said in a statement: "Arsenal manager Arsene Wenger and midfield player Samir Nasri have both been suspended for one UEFA club competition match following charges of improper conduct. The Arsenal manager has also been fined €10,000.
"An appeal may be lodged against the ruling within three days of the dispatch of the reasoned decision."
Wenger - who will not be allowed to go into his team's dressing-room, the tunnel, or the technical zone, or on the pitch, nor to have any form of communication with his team - had reiterated in his press conference prior to the announcement that he felt he did not deserve punishment.
"If I am punished it will be one of the very few times that I feel I don't deserve it, because I don't feel I did anything wrong," Wenger said. "I have no chance to speak my mind and I will have to accept it, but frankly I don't feel wrong and you don't feel at ease if you know you have done something wrong.
"This time I am quite relaxed, I don't even listen to what they have to say because I know what I've done and what I have said. I don't feel in this story I will have to be the one to be punished."