The groups' Lose the Lads' Mags campaign says displaying such publications, or asking staff to handle them, could see them sued for sex discrimination or sexual harassment.
They have obtained legal advice from equal rights lawyers, who wrote an open letter printed in today's Guardian calling on retailers to stop selling the magazines.
UK Feminista and Object may bring a test case against retailers who fail to act and the groups say they will support employees who are uncomfortable with images of naked or near-naked women on magazines, the newspaper said.
Sophie Bennett, campaigns officer for Object, added: " Lads' mags dehumanise and objectify women, promoting harmful attitudes that underpin discrimination and violence against women and girls.
"Reducing women to sex objects sends out an incredibly dangerous message that women are constantly sexually available and displaying these publications in everyday spaces normalises this sexism."