"Barnsley Football Club can confirm that it has lodged a formal complaint to both the English Football League and the Football Association," the club said in a statement.
"This is following an alleged incident at the conclusion of the match on Saturday 13 April, between Joey Barton and Daniel Stendel."
Barnsley won the game 4-2 after Fleetwood had defender Harry Souttar sent off after 65 minutes.
The club also said they were working with the police to assist with all enquiries and would not make any further comment on the matter while the investigation remains ongoing.
On Sunday, Fleetwood said they were "establishing the facts" and would not make any further comment.
Barnsley are currently second in the League One standings while Fleetwood are 11th.
(Reporting by Rohith Nair in Bengaluru; Editing by Christian Radnedge)
