The fire in Wolfe Road Park, Wolfe Road, Foxhill, was reported at 7.30pm last night.
Firefighters extinguished the flames.
Sheffield firefighters also dealt with wheelie bins set alight in Station Road, Chapeltown; Angleton Green and Queen Mary Road, both on the Manor estate.
A skip was set alight in another arson attack in Station Road, Mexborough, Doncaster.
Anyone with information should call South Yorkshire Police on 101.