The Greens, RSPCA and a leading activist are calling for the ban after a young bull was euthanised after injuring its leg at an event at the show on Friday.

However, co-owner of the MC Rodeo Company Mick Wyllie says a ban is "very unnecessary" and rodeos are growing in popularity in Tasmania.

Primary Industries Minister Guy Barnett said under the Animal Welfare Act Tasmanian rodeos had to be run under a "prescribed code of practice".

"Biosecurity Tasmania is following up with the attending vet and will consider if any further action is required. The government will not be banning rodeos."

Greens leader Cassy O'Connor said rodeos were cruel and the death highlighted the need to ban them.

"These injuries and deaths happen at rodeos on a regular basis, around the country and in Tasmania," Ms O'Connor said.

"It's a tragic but inevitable outcome, when you frighten and torture animals for 'sport'.

"It is animal mental suffering for the sake of money in the name of entertainment."

Ms O'Connor said a ban was long-standing Greens' policy and a key part of the party's Animal Welfare Amendment Bill.

Mr Wyllie said injuries were "very rare" and less than in normal rural production.

"We love our animals and we invite people to come to visit us and come to our rodeos to see how they are treated," Mr Wyllie said.

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"Our crowds are very strong at the moment, people want to come back to rural settings and we always have extremists who want to ban them.

"It is the old squeaky wheel that gets the oil but sometimes they over oil."

Mr Wyllie rejected suggestions the injured bull had been left to suffer.

Rodeos were becoming so popular that 12 events would be held in Tasmania between now and March next year and attracted up to 6000 people, he said.

"We only do it for a hobby, not for money as some people say," he said.

"Rodeos inject hundreds of thousands of dollars into local communities."

The founder of Brightside Farm Sanctuary Emma Haswell said she had been inundated with hate mail since posting a video on social media of the bull and was adamant rodeos needed to be banned.

"They prey on the vulnerability of the animals to perform out of terror," Ms Haswell said.

"They use ropes and spurs and these animals are goaded and tormented into a frenzy before being let out of the chute and are ready to explode they are so wound up.

"It is indefensible on every level. They only have a vet at rodeos because we lobbied for that many years ago."

RSPCA chief executive Dr Andrew Byrne said he was against rodeos and using animals for entertainment.

"I would love to see a ban, it makes no sense," Dr Byrne said.

"It is a reckless activity that relies on fear.

"There is a culture among a small group of people who follow rodeos religiously."