The attack happened between 4pm and 5pm on Thursday, July 10.
The woman, who is in her 40s, was walking along Heigham Street when a large dog, believed to be a Bull Mastiff, ran towards her in an aggressive manner. It then jumped up onto her, causing her to fall into the road.
The owner of the dog then appeared and put the dog on a lead before heading into the direction of the city centre.
The victim was taken to the Norfolk and Norwich Hospital where she continues to receive treatment for a fractured vertebrae.
The owner of the dog is described as tall, well dressed and in his late 30s. The dog is described as a dark brown/black Bull Mastiff.
PC Scott Ellis said: “I would ask for anyone who saw this incident or with information to contact police. This has been a distressing incident for the victim who now faces some considerable time in hospital being treated for her injury.”