Lancashire Constabulary are investigating after Burnley and Cardiff supporters clashed outside Turf Moor on Saturday.
A video circulated on social media appears to show a group of fans fighting after the game, with one man apparently knocked unconscious after hitting his head on a wall.
A police spokesman told Press Association Sport they were aware of the incident but no serious injuries had been reported to them.
The police are also looking into offensive social media posts made after the Clarets’ 2-0 win over their relegation rivals.
“Burnley FC is aware of a post-match incident involving two sets of supporters outside Turf Moor after Saturday’s game with Cardiff City,” said a statement from Burnley.
“In addition, a number of offensive posts have been reported to the club, and we are working with Lancashire Constabulary on both these issues.”
Meanwhile, the Clarets are to subsidise tickets for next month’s trip to Everton as part of their ‘Chairman’s Pledge’ initiative with adult prices capped at £10 and concessions £5, matching the offer for Easter Monday’s trip to Chelsea.
“We have been delighted at the take-up for tickets for the game at Chelsea, but equally we are aware of the distance and travel difficulties involved,” chairman Mike Garlick told burnleyfootballclub.com.
“We would therefore like to extend this offer for a game much closer to home, to enable as many supporters as possible to cheer the team on in our final away game of the Premier League season at Everton.
“We all appreciate the effort and expense it takes to follow the team on the road and hope this offer will repay you for your loyalty and continued support.”