Gog the Yorkshire terrier became well known in Leicester 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 the Haymarket Shopping Centre on Friday.
She left Gog in her buggy outside and CCTV shows a woman wheeling it away.
Ms Shortt, 69, said she needs to get her pet back urgently because Gog needs surgery on her knees costing over Â£1,000.
"I haven't been without her since I've had her," said Ms Shortt.
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"We come into town regularly and she lights everybody's day up.
"People say they love seeing her and hundreds of people have taken pictures of her."
Gog was wearing a jumper, spotty baby vest and ribbons in her hair when she was stolen.
She is five years old and Ms Shortt has owned her since just before she was seven weeks old.
Ms Shortt uses the buggy to help her carry things and Gog sometimes sits inside.
Leicestershire Police is examining CCTV of the theft, which happened in Humberstone Gate at about 14:50 GMT on Friday.
Ms Shortt's coat, bag and inhalers were also in the stolen buggy but she is only concerned about getting Gog back.

Rouken Glen Park in East Renfrewshire, which was originally gifted to the people of Glasgow in 1906, was named the UK's Best Park of 2016.
The shortlist for the Fields in Trust award included Castle Gardens in County Antrim, Pontypool Park in Torfaen, and Preston Park Rockery in East Sussex.
Fields in Trust was established in 1925 by King George V as the National Playing Fields Association.
Rouken Glen Park is a 143-acre historic park located next to Thornliebank, Giffnock and Newton Mearns, about six miles to the south of Glasgow city centre.
The award came after the completion of a Â£3m transformation project in the park.
Fields in Trust chief executive Helen Griffiths said: "It's a beautiful green space and well-deserving of the accolade. The number of parks nominated this year and the votes cast across the competition show just how much the public cherish their local green spaces.
"The people of East Renfrewshire have sent a clear message that they love their local park and I hope that East Renfrewshire Council will recognise this by working with us to safeguard Rouken Glen Park as a place for community sport, play and recreation forever."
East Renfrewshire Council parks manager Donnie McManus said: "We would like to thank everyone who voted for the park. Also a big thanks to all the staff who work tirelessly in the park, keeping it up to a very high standard.
"This award shows that the public of East Renfrewshire and the many visitors to the park hold it in such high esteem."
Councillor Vincent Waters, East Renfrewshire's convener of environment, added: "Rouken Glen has always held a very special place in the hearts of all its visitors and now it's official - it's the best park in the UK.
"This is a fantastic accolade to win and is just reward for all the hard work our dedicated staff and volunteers have put in to improving the park over the last few years.
"It has unrivalled natural beauty and there is something for all ages to enjoy. Rouken Glen has been loved by all for more than 100 years, and will continue to attract thousands of visitors to East Renfrewshire in the years to come."
A dog that became a local celebrity has been wheeled off in a buggy by a mystery woman, sparking a hunt for the animal's return.
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A Scottish park has been recognised with a top UK award.