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."