Locks and fencing have been damaged at the Saxby Road playing fields site with some of the incidences taking place were training and playing matches.
Officers have appealed for information from the public on the offences and offenders in a bid to stop them happening.
Pcso Emma Prothero, of the Melton Town South beat, said: “We have received reports of anti-social behaviour and criminal damage at Melton Town Foxes Football Club on Saxby Road.
"Some of the incidents have occurred while training sessions and matches are in progress.
"When the suspects have been challenged they have become abusive, sometimes in front of young children and their parents.
"The club are grass roots and trying to provide a service to the local community, they don’t need the added cost of repairing fencing and buying new locks.
"At the moment they are trying to fix patches of grass which is being hindered by the trespassers.”Aside from the damage and public order incidents, the club has a problem with people trespassing and leaving litter at the site.
Pcso Prothero added: “We will be increasing our patrols and holding some engagement events in the future.
"If anyone witnesses unauthorised use of the field and anti-social behaviour we would ask them to please report this at the time to us on 101.”
The club has been running since 1985 and has football teams ranging from six-year-olds to teenagers.