Rotherham United plan to bans fans involved in opening-day crowd trouble
Following the 1-1 draw, trouble flared between rivals supporters in the corner of the ground between the family stand and the away end.
The issue is believed to have involved Swansea flags, although neither of the clubs or the police have confirmed this.
The Millers subsequently released a statement in which they said they were "incredibly disappointed" with the actions of "a small number" of their followers.
They added: "Both clubs will now work together alongside South Yorkshire Police to identify and subsequently punish the perpetrators.
"The individuals in question will not be welcome back at AESSEAL New York Stadium, where we pride ourselves on creating an environment in which everyone can enjoy the game.
"We would like to thank the majority of our fan base who – as always – behaved impeccably and helped the team to perform on the pitch."