Investigators have been told an unknown woman and young boy entered the front garden of a Stawell Street property between 3-3.30pm and patted the dog.
The two then picked up the dog and started to leave the property when the owner came out to stop them.
The offenders left with the dog.
Molly the 7-year-old Maltese Terrier is the loving companion of a 79-year-old woman who has dementia.
Police have released images of Molly in the hope that someone has information on her whereabouts.