Roads around Leppings Lane in Hillsborough were closed after the bomb was found by council workers carrying out a routine inspection of pipes.
South Yorkshire Police confirmed the Explosive Ordinance Disposal team had been called out to assess the situation.
"Officers are attending at the river bank of the River Don near Leppings Lane, Hillsborough, after being alerted by Sheffield City Council during a routine inspection of pipes to what is believed to be an unexploded device," said a police spokeswoman.
"Nearby roads will be sealed off while an inspection is carried out."
No new date has yet been given for the rearranged fixture.