The Equalities Minister and LibDem MP for East Dunbartonshire appealed to them to "shed fad diets and fitness myths" in the new year and "celebrate the beauty of diversity in body shape, skin colour, size and age".
In an open letter she said: "As editors you owe more to your readers than the reckless promotion of unhealthy solutions to losing weight."
Ms Swinson, who is concerned about unrepresentative images of thin women being too pervasive in the media, said there is a problem with the promotion of new diets at this time of year.
Tips on losing weight are targeted at people who have eaten rich food at Christmas and are ready to make new year resolutions for self-improvement.
"We're all aware that there are no miracle diets or if there are, they are miracles that come with a cost," said Ms Swinson.
But critics pointed out that Ms Swinson's letter may be too late for the January magazines – which have already been written.
The former editor of NME music magazine Conor McNicholas said: "Dear Jo Swinson, want to start telling mag eds what to do? You might want to learn a bit more about their monthly lead times."