The Daily Mail says Stendel and Barton clashed in the tunnel following the clubs' League One match on Saturday afternoon.
A club statement read: "Barnsley 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 while police investigations are ongoing."