South Yorkshire police said they were investigating an incident in the tunnel at Oakwell that allegedly left Barnsley counterpart Daniel Stendel with facial injuries following Saturday's League One match.
Bauer strikes at the death to send Charlton into the Championship
"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.
Sunderland shackle Portsmouth to reach League One play-off final
Attendance watch: More fans watch League One Sunderland than Tottenham