Eduardo handed two game ban
Arsenal have three days to appeal against the punishment for the Brazilian-born Croatian international, UEFA said in a statement.
Eduardo went down in the Celtic game after poking the ball past goalkeeper Artur Boruc, who dived at his feet but appeared to make little or no contact with the striker.
Eduardo, who spent a year out of the game after suffering a badly broken leg in February 2008, converted the penalty himself to put Arsenal 1-0 ahead and 3-0 up on aggregate, effectively killing off Celtic's hopes of saving the tie.
The English side eventually won 3-1 for a 5-1 aggregate win.
The decision to take action against Eduardo infuriated Arsenal manager Arsene Wenger who described it as disgraceful and accused UEFA of launching a witch hunt.
Eduardo will miss Arsenal's first two Group H matches away at Standard Liege on September 16 and at home to Olympiakos on September 29.