Bella, a two-year-old American bulldog, was reportedly taken from Auckland Road in Mexborough, near Doncaster, at around 3pm on Christmas Day.
South Yorkshire Police is appealing for anyone who may have seen a man, described as being white, in his 20s, with brown hair, of thin build, and around 5ft 8ins tall, in the area at the time to contact them.
Bella was wearing the brown harness seen in the photograph (above), with a gold plate on the front.
A statement from the force said: "Did you see Bella being walked on Christmas Day in the afternoon? Have you seen a dog like Bella since, or been offered a dog like Bella for sale?
"If you have any information, please call police on 101 quoting incident number 582 of 25 December 2020. You can also give information anonymously to independent charity Crimestoppers via their website – www.crimestoppers-uk.org – or by calling their UK Contact Centre on 0800 555 111."