Barnsley have made a formal complaint to the English Football League and Football Association relating to the alleged incident involving their manager Daniel Stendel and Fleetwood Town boss Joey Barton following Saturday's League One game at Oakwell.
South Yorkshire Police are also investigating the matter.
A statement issued by Barnsley read: "Barnsley Football Club can confirm that it has lodged a formal complaint to both the English Football League and the Football Association.
"This is following an alleged incident at the conclusion of the match on Saturday 13th April, between Joey Barton and Daniel Stendel.
"The club is also currently working with the police and assisting with all enquiries regarding the incident.
"No further comment will be issued whilst police investigations are ongoing."
Following Barnsley's 4-2 win, their striker Cauley Woodrow suggested Barton confronted Stendel in a now-deleted tweet.
Sky Sports News showed footage after the match that appeared to show former Newcastle United, Marseille and Manchester City midfielder Barton attempting to leave the ground in a car before being stopped by police.
Neither Barnsley nor Fleetwood fulfilled their post-match media duties after the game, where victory moved the Tykes back into the second automatic promotion place.