The family of John Gordon – East Kilbride's first Provost – are appealing for help to find their thoroughbred Lhasa Apso, which is named Buster.
Mr Gordon, 90, died on April 27 and his funeral was held at South Lanarkshire Crematorium, Blantyre, last Thursday.
His son, also John, said Buster was stolen from an East Kilbride supermarket car park while the service was taking place.
He and wife Teresa, 57, desperately want their pet back.
Mr Gordon, a 60-year-old computer information consultant, said Buster cost £400 and he suspects the thief or thieves will try to sell him.
Mr Gordon said: "It had been a long day at the funeral and my grandson was tired, so my wife took him home early.
"They stopped at the Co-op in East Kilbride Village to buy him a packet of sweets and tied Buster outside. He can be a yappy wee thing around other dogs so she purposely tied him up away from the front of the store.
"When they came out, he and his lead were nowhere to be seen.
"They were not in the shop for longer than 10 minutes and my wife said it was fairly busy at the time. Buster was tied up tightly so could not have escaped by himself."
At the time, Mr Gordon was still at the humanist funeral service, which he conducted himself.
His father became Provost of East Kilbride in 1963 after campaigning for the town to become an independent burgh.
His son added: "It was already a very emotional day, so to find out Buster was gone just topped it off. You would never think people would do such a thing.
"It was horrible when we realised he was gone. He's a lovely little dog."
Buster is golden in colour and when he went missing he was wearing a red collar with a green lead attached.
Anyone with any information is asked to contact John directly on 07799895464 or call police on 0141 532 2000.
CAN YOU HELP FIND BUSTER?