Barnsley and Leeds United are “working together” to assess crowd trouble that marred Sunday’s derby clash at Oakwell.
South Yorkshire Police also launched an investigation following the arrest of three people on suspicion of public order offences and a man on suspicion of assault.
Leeds fans clashed with stewards in the away end towards the latter stages of their side’s 2-0 win.
Fighting also broke out in the East Stand.
“Barnsley Football Club and Leeds United Football Club are greatly disappointed by reports of violence at yesterday’s game and will be working together to assess the matter,” a statement said.
Trouble flared shortly after Eddie Nketiah fired the visitors into an 84th-minute lead. Mateusz Klich’s late penalty sealed the win for Marcelo Bielsa’s side.
Following reports a steward had been assaulted in the ground towards the end of the match, a 24-year-old man was arrested on suspicion of assault.
He has been released under investigation and is believed to be a Leeds fan, said West Yorkshire Police.
Two men in their 40s, also thought to be Leeds fans, were arrested on suspicion of affray following reports of a disturbance in the ground at the end of the match. They have been released as inquiries continue, said the force.
A fourth man was arrested on suspicion of a public order offence following the match on Schwabisch Gmund Way. He is believed to be a Barnsley fan, police said.
Victory moved Leeds back to the top of the Sky Bet Championship, ahead of Swansea on goal difference.
Barnsley, promoted from League One last season, slipped into the bottom three after four defeats and two draws since their opening-day win against Fulham.