Dida went down after a Celtic supporter ran onto the pitch in the final stages of the match and appeared to make light contact with the Brazilian.
AC Milan immediately issued a statement on their Web site (www.acmilan.com) saying they would appeal the ban.
"AC Milan announces that it intends to appeal to the UEFA Appeals Commission against the two-game ban inflicted on Nelson Dida," the statement said.
The ban was later described as "absolutely excessive" by club lawyer Leandro Cantamessa.
"It seems like a very, very unbalanced sentence," Cantamessa told Italian media. "Dida has become the protagonist of the episode while the protagonist is another.
"This is not correct from my point of view of logic."