Flora, a young lurcher, Harry, a wire-coated lurcher cross collie, Prince, an 11-month-old Saluki, and Bassett, a two-year-old Patterdale cross, have all disappeared.
Animal care manager at the home Jackie Dalton said she was hopeful that a member of the public would be able to come forward with information for their safe return.
She said: “The police have been informed and we hope by publicising this we will get them returned as soon as possible.
“In the past when we have had dogs stolen thanks to all the publicity given to it by the local media they were safely recovered and the thief prosecuted.”
It is thought the thieves climbed over the fence near the football field and kicked down the doors to the kennels to steal the animals.
Their disappearance was only discovered when staff arrived at the home around 5.30am, so it is not clear exactly what time the thefts happened.
The missing animals are described as “nervous” and workers at the home are keen to see them returned safe and well.
The Claverton Down animal care centre looks after and rehomes around 25,000 unwanted pets every year, making it one of the largest of its kind in the UK.
Anyone with information is asked to contact Bath police on 0845 4567000, or Crimestoppers anonymously on 0800 555111.