Police said on Monday they made nine arrests following Manchester United's intense 4-2 Premier League win over Leeds United during which a Manchester player appeared to have been hit by something thrown from the crowd.
Second-half goals from substitutes Fred and Anthony Elanga earned Manchester victory on Sunday in the red-hot atmosphere, and academy graduate Anthony Elanga appeared to have been hit by something while celebrating Fred's goal.
Manchester United and Leeds have had a fierce rivalry over the years, with the fixture sometimes called the Pennines derby.
"There was no significant disorder but there were a few incidents in Leeds City Centre ahead of the game and some minor incidents throughout the game," West Yorkshire Police said in a statement.
"Officers were deployed in sufficient numbers to rapidly intervene to identify and arrest the people responsible and prevent any escalation in disorder."
"The majority of fans on both sides behaved appropriately throughout the match and there was no significant disorder, but we hope the early intervention and positive action ... will help send a very clear message," Deputy Chief Constable Russ Foster added.
According to media reports, the Football Association is aware of the incident involving Elanga and is looking into it, with Manchester United manager Ralf Rangnick and Leeds boss Marcelo Bielsa condemning the action of supporters involved.
"Obviously things like that should not happen and I think ever more so in this game, the atmosphere was great at times we had to cool down," Rangnick said.
Bielsa said after the match that he had not seen the incident but added that violence in football "should not be approved".