The Co-operative has given so-called lads' mags six weeks to cover up their front pages with sealed "modesty bags" or be taken off sale in its stores.
The 4,000-outlet retailer said it was responding to concerns by its members, customers and colleagues about images of scantily-clad women on covers.
Titles such as Front, Loaded, Nuts and Zoo have been given a deadline of 9 September by the Co-op.
An industry body said the titles showed the "diverse interests of young men".
The Co-op, which is owned and run by its more than seven million members, introduced opaque screens for lads' magazines on some shelves earlier this month.
Steve Murrells, retail chief executive for the Co-operative Group, said: "As a community-based retailer, we have listened to the concerns of our customers and members, many of whom say they object to their children being able to see overt sexual images in our stores.
"Whilst we have tried to mitigate the likelihood of young children seeing the images with a number of measures in store, the most effective way of doing this is for these magazines to be put in individual, sealed modesty bags."
Cathryn Higgs, a policy manager at the Co-op, told BBC Radio 4's Today programme the group was currently "in dialogue" with the magazine publishers.
"I've got every hope they will take what we believe is the responsible approach and put them in a bag," she said.
She added that the Co-op believed it was the first retailer in the UK to take this step but other supermarkets were probably having "similar conversations with their customers".
The Daily Sport newspaper has already agreed to comply with the Co-operative's new policy.
'Like wallpaper'
Women and Equalities Minister Jo Swinson said the Co-op's move was "very welcome".
"Many parents aren't comfortable with the way sexualised imagery has become like wallpaper - everywhere from the bus stop to the corner shop," she said.
"Adults should be left to make their own decisions about what legal sexual images they look at, but the place for these is not next to the sweets at children's eye-level. I hope other retailers will follow the Co-operative's lead."
But campaign group Lose the Lads' Mags said the Co-op was not going far enough.
Spokeswoman Sophie Bennett said: "The so-called 'modesty bags' they are demanding from publishers are designed to allow the Co-operative to continue profiting from sexist, harmful lads' mags - but just a bit more discreetly."
Fellow campaigner Kat Banyard added: "Lads' mags are deeply harmful.
Glamour model Natalie Rochford, and Kat Banyard, who represents the Lose the Lads' Mags Campaign
"By portraying women as dehumanised sex objects, they send out the message that it's normal and acceptable to treat women this way, and we know from extensive evidence that lads' mags like Nuts and Zoo fuel sexist attitudes; attitudes that underpin violence against women."
The campaign group said it had also been targeting Tesco, with one female shareholder raising the subject during the retailer's recent annual general meeting.
The Professional Publishers Association, which represents some magazine publishers, said: "Men's lifestyle magazines are mainstream titles enjoyed by a readership of millions and feature content to reflect the diverse interests of the nation's young men.
"Publishers support the guidelines on the appropriate display of men's lifestyle magazines, which have been drawn up with the National Federation of Retail Newsagents and endorsed by the Home Office."
A former editor of Front magazine, Piers Hernu, said the Co-op's decision was "very dangerous" and amounted to "censorship".
The firm had "caved in" to a "vociferous campaign from some fanatical feminists", showing itself to be "weak-willed and spineless", he argued on BBC Radio 5 live.
Gender equality groups UK Feminista and Object joined forces with lawyers to launch the Lose the Lads' Mags campaign earlier this year.
They warned that retailers could face legal action if they continued to display the magazines or require staff to handle them.
This, they said, could amount to sexual harassment or discrimination in breach of the Equality Act 2010.
The British Retail Consortium has said its members do not sell anything illegal and have long followed industry rules.
