The incident happened at around 4.40am this morning (Thursday), while the victim was walking between Cayton Low Road and Morrisons in Eastfield.
Police said she was approached from behind, possibly by two people, and forced to the ground while walking through a snicket at the side of the A64.
Her handbag was then stolen before the suspects fled towards Cayton Low Road.
A North Yorkshire Police spokesperson said: "The victim sustained only minor injuries but is understandably very shocked and upset.
"The handbag is black with a flap-over fastening. It contained a silver matchbox-sized tobacco tin which does not fully close and other personal possessions including paperwork.
"The Serious Crime Team in Scarborough is investigating this incident and appealing for information, specifically any sightings of people acting suspiciously in the area, or anyone with information about the people involved."
Anyone with information is asked to contact North Yorkshire Police on 101, quoting reference number 12160172574.