Last month, UEFA confirmed an investigation had been launched into "events involving supporters which occurred inside and around the stadium".
An ethics and disciplinary inspector was appointed by UEFA to look into the events that took place around the 1-1 draw between England and Italy, who prevailed on penalties.
And a brief statement released on Tuesday confirmed proceedings had been opened against the FA for a "potential violation of Article 16(2)(h) of the UEFA Disciplinary Regulations for a lack of order or discipline by its supporters".
Damage was caused prior to the match as a number of supporters were seen clashing with security as they tried to enter the stadium in north London without tickets.
The FA launched its own independent review into what it described as "disgraceful scenes".
UEFA previously fined the FA €30,000 (£25,600) for three offences stemming from England's semi-final win over Denmark, which saw a laser pointer directed at Denmark goalkeeper Kasper Schmeichel prior to a penalty for the hosts.