Dida was suspended for pretending to be injured after being touched on the face by a Celtic fan who ran onto the field during Milan's 2-1 loss in Glasgow on Oct. 3.
Milan vice president Adriano Galliani said that Dida traveled with team lawyer Leandro Cantamessa to UEFA headquarters in Nyon, Switzerland, for the appeal.
"We're satisfied with the reduction of one game," Galliani was quoted as saying by the ANSA news agency. "It's fair that he's banned for one game, because he made a mistake. But not having hurt anyone, not being an act of violence, for us there were not the extremes for two games."
Dida will miss Wednesday's match with Shakhtar Donetsk at the San Siro, but will now be able to return when the Rossoneri face Shakhtar in Ukraine two weeks later because of UEFA's ruling.
The incident occurred when the fan ran onto the field at Celtic Park in the 90th minute and made what appeared to be minimal contact with Dida's face.
The Milan goalkeeper then turned to chase the fan before dropping to the ground. He was carried off the field on a stretcher with an ice pack pressed to his cheek, and was replaced.
Celtic was fined 30,000 Swiss francs (US$25,400; €17,840) for the incident and will have to pay an additional 30,000 francs (US$25,400; €17,840) if it fails to control its fans again in the next two years.
The 27-year-old fan who invaded the field was later arrested and banned for life by Celtic.
Before Milan's 1-0 loss to Empoli on Sunday, Dida gestured to fans at the San Siro in a praying gesture - turning to all four sides of the stadium with his hands held together - to ask forgiveness. The crowd applauded him.
"At this point, the relationship with the fans is mended," Galliani said. "The club didn't ask him to make the gesture - I certainly didn't. It was a spontaneous gesture."
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