An investigation will be conducted regarding the incidents which included a group of visiting fans wrecking a bar area and stealing food and money.
It is believed that catering staff had to barricade themselves in a store room when fans broke.
A South Yorkshire Police statement released on Wednesday morning said: "South Yorkshire Police can confirm a disorder occurred during the first half of the Barnsley versus Manchester United match at Oakwell last night.
"Police and both football clubs were disappointed by the conduct of a minority of fans.
"Police responded quickly and effectively to a spontaneous disorder caused by a small group of people that had gathered near to the central bar on the North Stand.
"Officers in protective uniform were deployed to restore order, disperse the crowd and ensure the safety of staff inside the area."
The FA are awaiting reports from their crowd control advisor as well as from referee Chris Foy.