Officers from North Yorkshire Fire & Rescue Service were called to save the pet on Thursday afternoon at a family home in Tadcaster, North Yorkshire.
The kitten, named Coco, had crawled under the living room sofa and moved its head into the furniture's mechanism, where it became stuck, the fire service said.
Officers spent more than an hour cutting through the sofa with hacksaws and bolt cutters after the owner told them they could do "whatever they needed" to free the feline.
Bob Hoskins, station manager prevention at North Yorkshire Fire & Rescue, said he had not seen such a case in his 23 years with the service.
"Small animal rescues are quite common," he said. "We get dogs stuck in holes, and cats up trees is a common one, but a cat in a sofa is a first."
The kitten was "wriggling around in panic" during the operation and "making quite a lot of noise", the fire service said, but received no physical injuries.
The pet's owner, who was left relieved after the kitten was safely returned, was forced to hold Coco still while officers dismantled the sofa.
Mr Hoskins said kittens are "naturally inquisitive at that age," advising owners: "You've just got to be aware that if you're sat on a chair, the cat might be underneath.
"It's a very rare occurrence, and fortunately on this occasion it all turned out ok."