Isla Kerr had just nipped into a nearby shop to buy an ice cream with her dad Darren, 33, when they left Dolly the Boston terrier tied up outside.
The seven-year-old came out of the shop in Sowerby Bridge, West Yorkshire, to find her dog missing.
The family have been desperately searching for three-year-old Dolly, who started to lose her sight this year.
Isla was so upset she told her mum Vanessa Meskimmon: "Santa can do anything," and then wrote a heartfelt letter to him.
She wrote: "Dear Santa, all I want for Christmas is my dog to come back. I do not care about presents all I care about is my dog Dolly to come home. I miss her so much and love her. Love Isla Kerr xxxx."
Mum Vanessa explained Isla and Dolly are like best friends and inseparable.
Police are currently investigating and have CCTV footage showing Dolly's thief as someone wearing grey jogging bottoms and a hoodie with a white logo.
Vanessa told The Daily Mirror: "We urge whoever has her to give her back, even if they just leave her somewhere she will be found.
"Please think about a little girl who wants her dog home for Christmas."
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