Both had been charged with improper conduct following their angry protests to referee Massimo Busacca at the end of the last 16 second-leg match at the Nou Camp on March 8.
Wenger, who was also fined 10,000 euros, subsequently accused European football's governing body of running a dictatorship.
"The UEFA Control and Disciplinary Body today decided to suspend Wenger and Nasri for one European match each, with the punishment applying to the next UEFA club game for which either man will be eligible," UEFA said in a statement following the decision by a disciplinary hearing at its headquarters.
Wenger described the decision by the Swiss official as "embarrassing" and was even more annoyed when UEFA decided to open disciplinary proceedings.
"We all understand that you can make wrong decisions but after that it becomes dictatorship, it's not any more common sense," Wenger said.
"It would be good for UEFA to show some humility, to apologise for what has happened."
