Pet owners in the Bridgewater area north of Hobart are being urged to keep their animals inside at night, amid fears pets are being deliberately set alight.

Tasmania Police and the RSPCA are investigating the claims after a pregnant cat suffered burns to the back of its head and neck.

It is believed Milly the cat, who is being nursed back to health by the RSPCA, was doused with accelerant before being set alight.

Its owners, who could not afford the vet bills, reported the incident to police and were forced to surrender the cat to the RSPCA.

Chief executive Peter West said it was very concerning.

"There's been some anecdotal reporting of small animals in the Bridgewater area being doused with petrol and set alight, so we're following up those allegations," he said.

Mr West said people should keep their pets inside at night for the time being.

"We've been told that a number of pet owners are ensuring their animals are inside at night, and that is certainly something we would be recommending — cats especially," he said.

Milly was able to safely give birth to her kittens. ( Supplied: RSPCA )

"Some indications are that this could just be children being naughty, but we would recommend that people certainly keep their pets close to home or keep their eye out."

Mr West said Milly nearly lost an ear but was slowly recovering and had given birth to three kittens since being set alight.

"We were quite concerned for Milly for a period of time but her wounds are healing quite well," he said.

"She's a beautiful cat and she loves her kittens and the three kittens are doing really really well."

Anyone with information is being urged to call the RSPCA's animal cruelty hotline or go to the website.