Lancashire Police are investigating footage posted on social media of fighting between Burnley and Cardiff fans on Saturday.
Video emerged of an incident as fans made their way out of Turf Moor following Burnley's controversial 2-0 win over Neil Warnock's relegation-threatened side.
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Multiple people became embroiled in the fracas with one supporter seen lying prone on the pavement after apparently being knocked down by two other men.
Lancashire Police have confirmed they are now aware of the incident and have launched an investigation.
A Burnley statement read: "Burnley FC is aware of a post-match incident involving two sets of supporters outside Turf Moor after Saturday's game with Cardiff City. In addition, a number of offensive posts have been reported to the club, and we are working with Lancashire Constabulary on both these issues."
Chris Wood scored both goals as Burnley moved towards mid-table safety with their third successive Premier League victory.
But it came with a deal of controversy as referee Mike Dean overruled his own decision to award Cardiff a penalty when Ben Mee appeared to head the ball on to his own hand - the score was 1-0 at the time.
Dean changed his mind on the penalty after consulting with assistant Darren Cann and Cardiff boss Neil Warnock said he would not comment on the call after having spoken to the FA about three other disciplinary matters earlier in the week.