The attack took place at about 5pm yesterday (September 11) outside the the Co-op store on Beckfield Lane in Acomb.
A spokesperson for North Yorkshire Police said: "The victim, a 71-year-old local woman, was taken to York District Hospital where she received treatment for her injuries, which thankfully are not as serious as first thought. She remains in hospital and is receiving support from specially trained officers."
A 22-year-old man from York has been arrested on suspicion of wounding with intent. He currently remains in police custody.
Police said no weapons had been used in the attack and officers believe it was an isolated incident.
Extra patrols are being conducted in the area to reassure the local community.