It highlights the Supreme Court's rulings on same-sex marriage earlier this week, with Sesame Street's Bert and Ernie cuddling as they watch a TV with the justices on the screen.
The New Yorker's website says the artist originally put the image on the social media site Tumblr.
Sesame Street did not respond to the New Yorker cover.
In the past, the organization has issued statements regarding the question of Ernie and Bert and sexuality.
Producers have said that puppets do not have a sexual orientation, and that Bert and Ernie were designed to teach their audience of 2- to 4-year-olds that people can be friends even when they are very different from one another.
Sesame Street says they have nothing to do with the cover photo and have no comment on it.
Some say lets keep it that way, but some people say just let them get married on the show.
"It's amazing to witness how attitudes on gay rights have evolved in my lifetime," said Jack Hunter, the artist of the photo.