William Gaillard has confirmed that Uefa will wait for the reports from the referee and match delegate before acting on the incident at Celtic Park on Wednesday night.
Gordon Strachan's side secured a dramatic UEFA Champions League win against Milan, but the game was marred by a Celtic supporter who entered the pitch during the celebration of Scott McDonald's goal.
The supporter ran onto the field and appeared to tap Milan goalkeeper Dida across the face.
The Brazilian momentarily chased the man, only to collapse holding the side of his face, before being stretchered off the pitch.
The incident has sparked fears that Celtic might face severe punishment, but Gaillard has confirmed that until the disciplinary board have analysed all the facts no action will be taken.
Gravity
The director of communications told Sky Sports News: "We need to receive the referee and delegate's report before the control disciplinary body decides whether to open an investigation.
"We should receive the report before the end of this week. Then one of our prosecutors will look into the document and will decide whether to open the investigation.
"If they open the investigation there needs to be a week or two before the disciplinary body deals with the case.
"There is a whole range of possible punishments.
"But of course they take into account precedence of the same type of incidents. And evaluate the gravity of the facts. This will be up to the disciplinary body.
"We all saw the same images; I don't want to presume on the opinion of the disciplinary body."
Detained
Meanwhile police have confirmed that they have yet to arrest anyone following the incident.
A Strathclyde Police spokesman said: "An incident occurred during the match. Police are investigating but nobody has been detained at present."