Uefa have opened disciplinary proceedings against Celtic following the incident in Wednesday's Champions League match, which saw a spectator confront Milan goalkeeper Dida.
Although Dida initially chased the fan, he then crumbled to the ground clutching his face before being stretched off with an ice pack.
Europe's football governing body have now asked Celtic to respond to charges of a lack of organisation and improper conduct of supporters.
Gordon Strachan's side have until 11th October, when the controlling disciplinary body of Uefa next convenes, to answer the charges.
However, there could still be repercussions for Dida, with Uefa also asking Milan to clarify why the Brazilian keeper was substituted following the incident.
With contact between the fan and the Milan keeper appearing to be minimal at best, the shot-stopper could well face action for appearing to embellish the severity of any injury.
Meanwhile, the fan involved Robert McHendry - has admitted breach of the peace at the Glasgow Sheriff Court.
He will be sentenced next month after reports.