Uefa has opened its investigation into the incident which saw a spectator confront AC Milan goalkeeper Dida at Celtic Park on Wednesday.
The player was carried off on a stretcher in the closing stages of Celtic's Champions League victory.
A disciplinary body will consult reports from the match delegate and referee Markus Merk.
Celtic are likely to be punished with a fine but Uefa could impose further penalties for the infringement.
The fan, who has since been identified and banned by the club for life, made contact with Dida who proceeded to briefly give chase before collapsing to the ground.
Contact appeared minimal and the Brazilian international has been roundly condemned for his theatrics.
Scottish Football Association chief executive Gordon Smith urged Uefa to punish the goalkeeper.
He would like to see similar action taken by the governing body who handed a two-match ban to Lithuania's Saulius Mikoliunas for diving in a Euro 2008 qualifier against Scotland.
Smith told the Daily Record: "I was at the match at Celtic Park but I did not see the fan come on to the pitch.
"From what I've been told he made what could be described as a friendly pat at the goalkeeper, who then decided to fall over.
"To see him leave the park on a stretcher could have been described as farcical.
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"I would hope that Uefa act in accordance with their recent judgment on Mikoliunas."
Smith added: "The fact of the matter is that Celtic will have a case to answer because their security was breached by the supporter who came on the park.
"Therefore there is nothing we can do to help them at this stage.
"What Uefa has to decide is whether Dida was guilty of simulation and whether it was intended to make the problem with the fan look even worse by indicating that he had been assaulted."
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