Zoo and Nuts will boycott the Cooperative Group, after it demanded they hide their magazine in so-called 'modesty mags' to stop children seeing their front covers.
The decision to boycott the shop instead of complying suggests the lads' mag market is becoming increasingly irritated by being sucked into a debate on the treatment of women in the media and children's access to sexually explicit images.
"Co-op's knee-jerk attempt to restrict access to a product that consumers have enjoyed for nearly a decade is wrong," Paul Williams, managing director of the Nuts publisher IPC Inspire, said.
"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 decision to boycott the shop could trigger a similar response from other magazines, such as Front and Loaded.
Such an eventuality would effectively amount to the magazines banning themselves from the Co-op shop – something many women's campaigners had originally wanted.
A spokesperson for The Co-operative said: "Our position has not changed. If Nuts, or any of the other publications, Zoo, Loaded and Front, do not put their titles into modesty bags by the date we've given of 9 September, we will no longer sell the magazines."
Zoo magazine says it has already toned down its covers in response to criticism.
"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," Williams said.
"We are delighted with our readers' response to the new covers and last week's issue was our biggest selling since February."
There have long been concerns about children's ability to see explicit and highly sexualised imagery on the front cover of lads' mags, but the issue took on a new importance amid the debate on online pornography.