Swindon Town Football Club has begun an investigation after seats were ripped up and thrown at Saturday's match against Bristol Rovers.
The club said that supporters from both teams were involved in the fracas at the County Ground.
It is now liaising with the police and will be searching through CCTV footage to identify any troublemakers.
A total of 11 arrests were made for assault, public order and drugs offences.
Some 130 officers from Wiltshire, Avon & Somerset & British transport police were on duty.
Swindon Town says it was taking the matter very seriously and will take action against anyone singled out.
Geoff Dunford, chairman of Bristol Rovers, told BBC Radio Bristol: "It is unacceptable. There were women and children sitting there. We are fully behind the Swindon investigation."
Swindon Town won the game, 2-1.