The dog was stolen from outside the Wellgate Shopping Centre, near to Wellgate Steps, at around 4pm on Thursday.
A force spokesman said: “The dog is described as a black and brindle Staffordshire Terrier, with a white chest and white paws. It has a ginger patch on it’s cheek and rear hip. At the time the dog was wearing a silver chain collar with a blue lead. If anyone knows where the dog is now, please contact Police Scotland, Tayside Division on 101.”