Scott Jamieson, 46, is desperate to be reunited with Leah – his Staffordshire bull terrier – seized at Constitution Street on Saturday.
The security guard had tied the six-month-old puppy to a hook outside Bishop Newsagent while he bought groceries at around 11am.
It was then that the thieves snatched the lead and made off with his dog.
And he believes the thieves had deliberately targeted his young dog.
Mr Jamieson, of Leith’s Cadiz Street, said he felt “lost” without his tan-coloured pet and issued a string of appeals on social media that have so far drawn a blank.
“The shop has special hooks to chain your dog to,” he said. “And they just unhitched it.”
Leah even accompanies her owner on night shift patrols at Dunedin FM Security and is with him 24 hours a day, leaving him “distraught”.
Police are investigating the theft and officers have advised Mr Jamieson to keep in regular contact with staff at the Edinburgh Dog and Cat Home at Seafield.
Mr Jamieson was diagnosed with Type 1 diabetes several years ago and said he took his new pet from his sister in a bid to exercise more.
“I’m a bit heartbroken,” he said. “She’s with me all the time.
“My sister’s dog had a surprise litter of puppies, and I used to dog-sit.
“As soon as Leah was able to leave my sister’s, she was with me.”
Mr Jamieson has made an emotional appeal to the dog thieves, urging them to return his pride and joy.
He said: “I think they saw me put Leah on the hook and just dived in and came in right behind me.
“Please, please give her back. I really don’t care how – I just want her back. She’s my life, full stop.”
He added: “The police have no leads just yet.
“I’m always hopeful but the longer it drags on, the more worrying it is. There’s no words to describe it – I’m just so gutted. It’s difficult.”
A police spokeswoman said: “Police are investigating following the disappearance of a Staffordshire bull terrier-type dog from outside a shop on Constitution Street on Saturday.
“The dog was left for a few minutes secured to a dog lead anchor point outside Bishop’s newsagents around 11am.
“When the owner came out of the shop two or three minutes later, the dog was gone along with its lead.
“The dog responds to the name Leah or Baba and is friendly. She is tan in colour with a distinctive white flash on her front, which tapers down to her belly.
“Her tail changes in colour from tan to black at the tip.
“The owner has searched for the dog and widely circulated its description on social media to no avail.
“We would urge anyone with any information about the dog or who was in the area at the time to contact Police Scotland on 101.”