He was carried off on a stretcher with an ice pack to his cheek.
Dida appeared to show no ill effects after the game.
"I'm making no excuses for the behavior, and the fan behaved disgracefully, but the contact made with the goalkeeper was minimal, absolutely minimal," Celtic chairman Brian Quinn said.
"Unless I missed something, he was carried off on a stretcher for what seemed to be the lightest tap you can imagine.
"The antics of the goalkeeper have to be taken into account."
Quinn said Celtic was investigating how the fan had been able to run onto the field and would take "appropriate action" against the man.
The fan avoid arrest after running off the field and police are still trying to locate him.
Milan said it would not appeal against the result of the match.
"The incident is unfortunate but it is the craziness of one single person," Milan organizing director Umberto Gandini said.
"We have nothing to say against anybody from Celtic.
"It is an individual case of misconduct."
Gandini said Dida would likely be fit for Sunday's Serie A match at Lazio.
Failure to control
UEFA said it was waiting for reports from match officials before deciding whether to launch an investigation.
Celtic could be charged with failing to control its fans.
"There is a whole range of possible punishments, but of course there are precedents for the same kind of incidents," UEFA communications director William Galliard said.
McDonald said UEFA should not let the incident affect Celtic's Champions League campaign.
"I hope the authorities are lenient," the Australia striker said.
"Dida has gone down as if he's been shot. It would be a tragedy if what happened affected the team."
Dida has been involved in similar incidents in the past.
The Brazilian was hit by a flare thrown by Inter Milan supporters during a Champions League quarterfinal between the local rivals in April 2005.
The match was abandoned and AC Milan awarded a 3-0 victory.
UEFA fined Inter $282,512 and made the club play its next four Champions League home matches behind closed doors.