The dead rabbit was found on Sunday morning on Fleetwood seafront with fireworks strapped to its body, as revealed in The Gazette on Tuesday.
Now a member of the public has put up £50 for anyone giving information leading to the conviction of the culprits.
Margaret Bysterbosch, secretary of the North Fylde RSPCA, said that the reward had been offered anonymously.
She said: "The person who rang me was very incensed about it – they were really annoyed.
"A number of people have mentioned it and everyone is angry. They think it's absolutely terrible."
The dead rabbit was spotted by a couple walking their dog early in the morning.
It was removed by a Wyre Council worker to avoid distress to passers-by near the seafront pitch-and-putt course.
Mrs Bysterbosch said that the rabbit looked more like a domestic pet than a wild animal.
She said: "It could have been stolen or it may have been released there.
"Sometimes if people want to get rid of a rabbit they will let it go there because they think it will be able to lead a natural life."