Wenger was unhappy with the performance of Damir Skomina and accused the Slovenian official of awarding too many free kicks to Milan, who lost 3-0 at Emirates Stadium in the second leg of the last-16 tie on March 6 but progressed 4-3 on aggregate.
"I was not happy with the referee because I felt he gave many free kicks in the middle of the park," Wenger said after the match.
"Every time (a Milan player) went down a free kick was given for them, and they sensed that very quickly and they used it very well."
Wenger is also alleged to have abused Skomina in the tunnel after his side were eliminated from Europe and will now be forced to watch from the stands for Arsenal's first three European fixtures next season, should they play that many.
A statement from the governing body read: "Arsenal FC manager Arsene Wenger has been suspended from carrying out his function for three UEFA competition matches by the UEFA Control and Disciplinary Body.
"Wenger has also been fined 40,000 euros. He was facing a charge of improper conduct in relation to the UEFA Champions League round of 16 second leg against AC Milan in London on 6 March.
"The suspension applies to the next three UEFA club competition matches for which Wenger will be eligible. An appeal may be lodged against the verdict within three days of the dispatch of the reasoned decision."
Speaking just before the news of the sanction was made official as he prepared for the Premier League trip to QPR, Wenger confirmed his intention to appeal if punished.
He said: "If I am [suspended] then it is not justified and I will appeal straight away. I believe that they have transformed UEFA competition referees to be untouchable icons, where you cannot even have a word.
"The only thing they understand after the game is the report. I believe that when you have 25 years consecutively in Europe you can still ask the referee that you can have some discussion with him. It is very difficult to understand."
Wenger was also banned for one match following his outburst at referee Massimo Busacca in the wake of Arsenal's Champions League exit to Barcelona last season.
He was then hit with a further two-game ban for contravening the initial suspension during the first leg of the club's Champions League qualifier against Udinese at Emirates Stadium at the start of this season.