Police are appealing for witnesses following the incident, which happened between 1.15pm and 1.45pm on Tuesday, May 31 in East Stevenson Street.
The cat, which was black and white, was so badly injured it had to be put down.
Officers are carrying out inquiries into the incident and are appealing for any witnesses to come forward and speak to them.
PC Dave King said: "The cat was so badly injured that unfortunately it had to be put down, and understandably the owners are incredibly distraught.
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"Our inquiries are continuing and we would ask anyone who has any information to get in contact."
Any witnesses should ring Northumbria Police on 101, quoting reference 798 310516, or Crimestoppers anonymously on 0800 555 111.