Gog the Yorkshire terrier became well known in Leicester city because her owner Monti Shortt dresses her in clothes and pushes her around in the buggy.
But the pooch was taken when the owner, who has cancer, quickly popped into a shopping centre on Friday.
She left Gog in her buggy outside and CCTV shows a woman wheeling it away, the BBC reported.
Shortt said she needs to get her pet back urgently because Gog needs surgery on her knees.
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"People say they love seeing her and hundreds of people have taken pictures of her," she said.
Gog was wearing a jumper, spotty baby vest and ribbons in her hair when she was stolen.
She is five years old and Shortt has owned her since just before she was seven weeks old.
Leicestershire Police is examining CCTV of the theft.
Shortt's coat, bag and inhalers were also in the stolen buggy but she is only concerned about getting Gog back, the report said.