In the process, he mocked well-known magazine editor Anna Wintour, who is not Vanity Fair's editor.
In a tweet, Trump contended that the magazine "is bending over backwards in apologizing for the minor hit they took" at Clinton in the video. He claimed that Wintour, a Clinton supporter, "is beside herself in grief & begging for forgiveness."
Vanity Fair's video posted over the weekend suggests New Year's resolutions for Clinton and encourages her to take up hobbies after her 2016 presidential election loss. Critics saw the video as sexist.
Vanity Fair then apologized, saying the attempt at humor "missed the mark."
Wintour is editor-in-chief of Vogue, not Vanity Fair, and is the artistic director of both publications' parent company, Conde Nast.
Vanity Fair's editor-in-chief is Radhika Jones, who succeeded longtime editor and Trump nemesis Graydon Carter earlier this month.