The Friends of King George V Playing Fields said the damage happened between 5.30pm on Saturday and 8.30am on Sunday.
The hives form part of an apiary established at the playing fields to produce honey which is sold through the site's Georgie Porgies cafe.
The Friends group said its beekeeper Chris Place and other members of the bee team were devastated by the damage after spending many hours tending to the bees and producing honey.
The information supplied does not state how many hives were damaged or how many bees were killed.
The Friends of King George V Playing Fields was established by Alan Fish in 2010 as a community group to improve and promote the playing fields.
Georgie Porgies cafe was set up in 2012 to raise money for the playing fields, with the apiary established later.
The group is appealing for information from anyone who saw people damaging the hives.
Information can be passed to beekeeper Chris Place at [email protected] or on 07771 540978.
People interested in volunteering at the playing fields or Georgie Porgies cafe can contact chairman Alan Fish at [email protected] or on 07931 765120.
