Nuts magazine has refused to cover up its front covers, meaning it will be banned from Co-op stores.
The lads' mag's publisher said the supermarket's "knee-jerk" action of demanding modesty bags was the result of protests by "niche lobby groups".
The Co-op gave magazines an ultimatum to cover up or face being removed from the shelves of its 4,000 stores.
Titles such as Front, Loaded, Nuts and Zoo - known for their pictures of scantily-clad models - have been given until September 9 to deliver the magazines in pre-sealed bags.
But IPC Inspire, the division of IPC Media which publishes Nuts, said it considered the ultimatum to be "an unreasonable attempt to prevent shoppers from freely browsing a legal magazine that is already displayed according to Home Office guidelines".
IPC Inspire managing director Paul Williams said: "The Co-operative's knee-jerk attempt to restrict access to a product that consumers have enjoyed for nearly a decade is wrong.
"Nuts takes its obligation to craft products that are right for consumers and retailers alike very seriously and for a number of weeks now we have had new covers in place, which have a more conservative tone. We are delighted with our readers' response to the new covers and last week's issue was our biggest selling since February.
"The objection that niche lobby groups have against certain sectors of the media should not mean that the right to purchase a perfectly legal product is restricted for the over half a million Nuts readers. As has been widely reported in the media in recent weeks, this is no longer a question of whether or not you like men's magazines, it is a question of how far you can restrict the public's ability to consume free and legal media before it becomes censorship."
The Co-operative, which describes itself as one of the UK's largest magazine sellers, had already introduced opaque screens on shelves last month to shield children from "lewd pictures" on front covers.
It comes amid increasing debate about the effects of sexual images on children, with David Cameron recently setting out a raft of reforms which will introduce family-friendly filters that automatically block internet porn unless customers choose to opt out.
Following the Co-operative's announcement, Tesco said it would only sell lads' magazines to over-18s.
The supermarket also said it had struck a "modesty deal" regarding the front covers of the magazines, and that Bizarre would be supplied in a bag.
Kate Jones, the Co-operative's head of product development, admitted that the store would lose money over the move.
Speaking on ITV's Daybreak, she said: "We will be losing money but we are responding to our customers' concerns.
"These are the publications that our customers are telling us they're concerned about.
"We do everything we can to ensure they are out of sight of children shopping in our shops.
"But sometimes during the trading day displays get disrupted.
"We think a modesty cover would be a fail-safe solution."