Chesterfield Borough Council made the plea amid fears over the birds' health and rats being attracted to the park.
Councillor Chris Ludlow, cabinet member for health and wellbeing, said: "We ask visitors to Queen's Park not to feed the birds, particularly the geese not only because the crumbs attract rats to the area but also because it is not healthy for the birds.
"Feeding them food such as bread can cause problems with their digestive systems and also affect their natural immunity.
"We do, though, encourage people to come along to the award-winning park and admire the wildfowl that live there."
Queen's Park was opened in 1887 to commemorate Queen Victoria's Golden Jubilee.