Saffy the cat, from Bradford, West Yorkshire, had to be rescued by a mechanic and needed to have a leg amputated after she hid under a car bonnet to keep warm.
The former stray is now recovering after being treated by vets at the PDSA but has been left scared of cars and going outdoors since the accident in November.
PDSA vet Rachel Bishop warned motorists to check under cars and wheel arches before driving.
"Sadly, it's not unusual for us to hear about this type of accident happening over the colder months. Cats often seek out warm places and a recently driven car engine can seem like a safe, cosy place for a snooze."
Saffy's owner, Shameena Baker, said the family pet had hidden underneath a neighbour's car bonnet.
Her thigh bone was severed when her leg got caught in the fan belt as the driver switched on the engine.
Ms Baker said: "Our neighbour heard Saffy scream when he turned the engine on.
"He turned it off straight away and opened the bonnet to find her tangled up and in anguish."
She added: "It was awful to see her and I didn't know what to do. We couldn't free her, she was so badly trapped, so we called a mechanic."
The mechanic freed Saffy, and Ms Baker rushed her to Bradford PDSA Pet Hospital, where she was immediately admitted for life-saving treatment.
A PDSA spokeswoman said: "Sadly, her leg was beyond repair and the vet team had no choice but to amputate."
She added: "Saffy has now made a full recovery and is managing great on three legs. However, the incident has left its mark on her - she is now scared of cars and mostly stays indoors."