Police said the meat had been left in the hedgerow and undergrowth at the beginning of the bridle path on Windmill Hill Lane in Chapeltown.
PCSO Deb Parker, from South Yorkshire Police's Sheffield North East Neighbourhoods Team, said: "Please be extra vigilant to ensure that your dogs are not eating anything when out walking.
"If you find anything, please contact 101 or report via the South Yorkshire Police website/report a crime."
She added that there had been one report received from a member of the public on Monday this week, but no dogs were believed to have fallen seriously ill.
She said she is not aware of any similar incidents in the area previously.