Seven men were arrested when violence broke out after Chesterfield's League Two match against Shrewsbury.
Groups goaded each other during the second half at the b2net stadium on Saturday, said police.
After the match, four Shrewsbury men were arrested when a Chesterfield man was assaulted in the stadium car park.
Two Chesterfield men were arrested on suspicion of public order offences while another local man was cautioned for running onto the pitch.
Those arrested on suspicion of assault are aged between 31 and 66, and have been released on police bail.
The two men suspected of public order offences, both aged 36, were also bailed.
Anyone with information about the incidents should contact Derbyshire Police.