It is alleged Ronaldo's conduct was improper and/or violent, the governing body said.
Ronaldo received a police caution in August after being interviewed by officers in relation to an allegation of assault and criminal damage following the incident at Goodison Park on April 9.
Footage was posted online of Ronaldo appearing to knock the supporter's mobile phone on to the ground as he walked toward the tunnel following United's 1-0 loss.
Under British law, a caution is essentially a warning given out by police for a minor crime if the person admits to the offense.
After the incident, Ronaldo issued a social media apology for his "outburst'' and invited the supporter to watch a game at Old Trafford "as a sign of fair play and sportsmanship.''
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