The incident came during the match against Fulham, which finished 1-1 in front of 10,000 returning fans.
One - named as Shaun Logan in an exchange with the player on Twitter - who was carrying a green-and-gold scarf, threw it towards Shaw as he went to take a set piece, with the scarf itself falling short and landing on the ground a few yards from the corner flag.
That reportedly saw him escorted from the game by stewards, with the fan later clarifying that despite being ready to head to Gdansk for the Europa League final next week, he had been told he was “facing a three-year ban” and that his “peaceful gesture...was taken out of context”.
The left-back, who was named on Tuesday as the club’s players’ player of the year, responded to the tweet to suggest he would intervene with authorities at United to have the potential ban removed.
“I understand completely, first match back at Old Trafford, emotions are high,” he wrote.
“I know there was nothing aggressive towards what you did. I will try my best to speak with someone and sort it out.”
The green-and-gold scarves are used by supporters in protest against United’s owners, the Glazer family.
There have been more protests since the Super League plans came to light and were quickly shut down, including the game against Liverpool being subsequently postponed and rearranged due to supporters getting inside Old Trafford and onto the pitch.
United will finish second in the Premier League this season and face Villarreal in the Europa League final on 26 May.
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