The Department of Agriculture is coming under pressure to take action against the Kilorglin Puck Fair.
The Animal Rights Action Network says it believes the practice of hoisting the puck above the street in an enclosure is a breach of new animal welfare rules.
The body had planned a protest at the annual event in Kerry for later today, but that has been postponed over safety fears.
Spokesperson John Carmody said they will now focus their efforts at a Government level.
He said: "Because we do believe that by using a puck in this fair this afternoon, that it is violating at least three parts of the five freedoms in the Animal Health and Welfare Act.
"We've been lobbying for years to get that, we got that in 2015 and now we're encouraging the Department of Agriculture to actually enforce these new laws."
Michael Healy Rae, the Independent TD for Kerry South, says fans of the Puck Fair will not be put off by the controversy.
He said: "Suggestions that people are going to be hesitant about going to the fair, they'll be looking at the goat and saying 'Oh you poor puck goat', that's a load of rubbish.
"There'll be thousands and thousands of people there, they've been there since early morning.
"There will be thousands of people there this evening to see a fine, healthy puck goat that has been treated well over the last numbers of weeks."