In response to the president's actions, Enrique Pena Nieto, the Mexican leader, cancelled a trip to Washington that was planned for Tuesday.
"It's a lack of sensitivity on the part of the publisher," said Guadalupe Loaeza, a Mexican author and columnist, according to the Guardian. "I started reading this and I couldn't finish. I didn't want to know anything about the wife of our country's No 1 enemy."
Social media users also weighed in, either mocking or criticising the editorial judgment of the magazine.
"Total lack of sensitivity," one Twitter user said in Spanish. Another called it the "worst timing in all editorial history".
Responding to the criticism, Vanity Fair Mexico issued a statement distancing itself from "offensive messages" published on social media.
"We understand the complicated moment that has coincided with the appearance of our cover, but our intention is simply to contribute, as always, an independent and critical point of view about current affairs and the people involved."
Earlier it tweeted: "No, this is not a story of flattery. We invite you to read the preview of this report on Melania Trump."
Mr Trump, himself, has been critical of Vanity Fair and has been particularly scathing of the editor Graydon Carter over the years.
The most recent outburst came last month when the then president-elect tweeted: "Has anyone looked at the really poor numbers of @VanityFair Magazine. Way down, big trouble, dead! Graydon Carter, no talent, will be out!"
This article was originally published by The Daily Telegraph.