United defender Kyron Gordon said he was targeted by an "idiot" Hull supporter during his team's 2-0 victory at City's MKM Stadium on Sunday, 4 September.
The 20-year-old, who was an unused substitute during the game and is the brother of Hull player Tyler Smith, was warming up on the touchline when he was allegedly abused.
Play was temporarily held up while the fourth official, a security officer and referee Matt Donohue were informed.
On Monday, Gordon tweeted that he was "disappointed" about what had happened.
But he added: "One idiot who’s ignorant doesn’t reflect the whole of hull city’s supporters, probably celebrating when a black player scores for his team. I know it will get dealt with properly. Thanks for all the messages."
United's win – thanks to goals from Sander Berge and Oli McBurnie – was Hull's third league defeat of the season and left the Blades top of the Championship by a point from second place Norwich.
City confirmed they were aware of the incident involving Gordon. A spokesperson added: "The club is working closely with both Sheffield United and Humberside Police to investigate."Humberside Police said in a statement: "We are aware of a reported incident during the second half of yesterday’s football match between Hull City and Sheffield United, which is said to have involved a Hull City fan and an opposition player.
"The club is working closely with both clubs to investigate the circumstances of the incident."
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