The Brazilian-born Croat fell in the penalty area in the 26th minute of the playoff second leg, which Arsenal won 3-1 for a 5-1 aggregate win.
He went down after poking the ball past Celtic goalkeeper Artur Boruc, who dived at his feet but appeared to make no contact with the striker.
The score was 0-0 at the time, with Eduardo converting the ensuing penalty to put Arsenal 3-0 ahead on aggregate which effectively killed off Celtic's hopes of saving the tie.
In a statement on their website, European football's governing body said: "UEFA has opened disciplinary proceedings against Eduardo for deceiving the referee, following the incident that brought about a penalty for his club in Wednesday's UEFA Champions League play-off against Celtic in London.
"Having studied video evidence of the incident in question, the UEFA disciplinary inspector decided to charge the player concerned. The UEFA Control and Disciplinary Body will examine the case on September 1."
If found guilty Eduardo could miss Arsenal's first two Group H matches away at Standard Liege on September 16 and at home to Olympiakos on September 29.
Arsenal manager Arsene Wenger told reporters after the match that he did not think a penalty should have been awarded.
"I do not go as far as to say Eduardo dived. He went down, for what reason I do not know. Having seen it again on television, it doesn't look a penalty," he said.
"I do not think he (Eduardo) would have complained if the penalty was not given."
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