South Yorkshire Police said over recent weeks a number of incidents have been reported at the Sandall Beat allotments, Intake.
Animals have been killed or injured and property has been damaged and stolen.
A force spokesman said: "Over the last few weeks there have been a number of break ins at Sandall Beat allotments.
"Property has been damaged and stolen and chickens, ducks and other livestock killed, injured or stolen."
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Anyone with information should call South Yorkshire Police on 101.