South Yorkshire Police said a 75-year-old woman was targeted in Dyche Road, Jordanthorpe, as she was walking away from a parade of shops.
A man asked her for bus money and when she declined, he grabbed her, put a knife to her throat and demanded her purse.
The 75-year-old woman wrestled with the robber before he ran off past Ladbrokes.
When the OAP returned home, she realised that her purse containing £10 was missing.
A South Yorkshire Police spokeswoman said: "At around 9am on Sunday, it was reported that the woman was walking away from the shops on Dyche Road in Jordanthorpe when she was approached by an unknown man.
"The offender is described as white, in his early 20s, around 5ft 6ins tall, skinny and spoke with a local accent.
"He was wearing a grey hooded top, grey tracksuit bottoms and was carrying a black Sports Direct bag.
"Were you in the area at the time? Did you see the robbery?
"An investigation is underway and officers are reviewing CCTV of the area."
Anyone with information should call South Yorkshire Police on 101 quoting incident 281 of October 22.