The victim, 79, was walking a Yorkshire Terrier on a lead when a woman walking a greyhound approached at around 3.30pm in Sewerby Road.
A Humberside Police spokesperson said: "
The greyhound then allegedly bit the Yorkshire Terrier and victim tried to intervene and was also bitten. The woman sustained injuries to her hands.
"A man who was in a red car helped the victim, as did a woman at a nearby address who assisted with first aid. We would like to speak to these two people and anyone else who saw the incident."
The incident happened on May 22.
Anyone with information is asked to call police on 101, quoting log 193 of 26/05/17.