Affco Talleys is trying to stop its workers talking about the company on Facebook and other social media, says the Meatworkers' Union.
The company has lodged papers with the Employment Relations Authority, in an attempt to get staff to 'desist' from posting comments about the company, the union said.
Union organiser Darien Fenton said the move was new territory.
"It's not concerning me that Talleys don't like what we say, but I think where we are heading with this is quite dangerous territory.
"If you look at the order, it's not only saying that the Union members, but its officers. Now up and down the country, the officers of the union are people that actually work for other companies. So they're saying that they want to control the commentary from all the other people."
Ms Fenton said the company was able to respond, using its own profiles.
In a statement Affco said the ongoing disparaging comments from the union breached obligations of good faith.
Earlier this month, the meat company said it was taking the union to the Employment Relations Authority over media statements.