Superintendent Dave Hall said: "The number of arrests, which currently stands at 21, were for public order offences, criminal damage, assault and breach of Section 27.
Humberside Police released a second statement after the game, which ended in a 2-1 win for Grimsby Town. It read: "Following the conclusion of the Scunthorpe United v Grimsby Town match at Glanford Park, police can confirm that no disorder was reported at the end of the match, and all supporters got away from the ground in a safe and peaceful manner.
"In order to minimise the potential of disorder at the Scunthorpe United v Grimsby Town football match at Glanford Park, police arrested a number of "potential risk" supporters and escorted them back to Grimsby.
"This group of 16 individuals, aged between 16 years to 28 years, were arrested to prevent a breach of the peace, after police believed they were intent on causing disorder in Scunthorpe and at the match.
"Once the likelihood of disorder had passed, the group had their tickets seized and were de-arrested.
"Shortly before the match kicked off, in a separate incident, two males were handed Section 27 dispersal orders.
"A short time later one of those males was then arrested for a breach of this order and taken into police custody.
"Another man was arrested for a report of criminal damage at Glanford Park."