Mia Merrill, a human resources manager at a Manhattan financial firm, started the petition against the work by Polish-French artist Balthasar Klossowski de Rola, known as Balthus.
The artist has long been controversial for his portraits of young girls in various states of undress.
It was his 1938 painting Therese Dreaming – which shows a 12-year-old girl wistfully looking up, her legs open and underwear visible – that prompted Ms Merrill to petition the museum to remove it from view, arguing that the Met was promoting paedophilia.
Therese Dreaming, a 1938 painting by Balthus, is the subject of debate at New York's Met museum
“I put together a petition asking the Met to take down a piece of art that is undeniably romanticizing the sexualization of a child,” she said, in a tweet.
“If you are a part of the #metoo movement or ever think about the implications of art on life, please support this effort.”
I put together a petition asking the Met to take down a piece of art that is undeniably romanticizing the sexualization of a child. If you are a part of the #metoo movement or ever think about the implications of art on life, please support this effort. http://bit.ly/2BzSEvg
Ms Merrill said she was “shocked” to see the painting depicting a young girl “in a sexually suggestive pose.”
She added: “Given the current climate around sexual assault and allegations that become more public each day, in showcasing this work for the masses without providing any type of clarification, The Met is, perhaps unintentionally, supporting voyeurism and the objectification of children.”
She clarified that she was not calling for the painting to be destroyed, but just removed from view or given additional context.
“I would consider this petition a success if the Met included a message as brief as, ‘Some viewers find this piece offensive or disturbing, given Balthus’s artistic infatuation with young girls',” she added.
Balthus has long been known for his controversial subjects.
In a 2013 review of the Balthus show in The New Republic, critic Jed Perl called Balthus the “last of the mystics who transformed twentieth-century art.”
Perl said mystics are “by turns revered, reviled, demonized, and ignored - and at one point or another in his very long career Balthus was regarded in all of those ways.”
He wrote that these works “can be properly appreciated only when we accept them as unabashedly mystical, the flesh a symbol of the spirit, the girl’s dawning self-awareness an emblem of the artist’s engagement with the world.”
In a piece entitled "Ol' Dirty Master," he wrote: “The original upskirt artist, Balthus devoted a career to obsessively depicting female pubescent sexuality. Today, there is no question that Balthus was a paedophile.”
Yet the Met issued a statement in response to the petition, refusing to remove the work from display.
“The Metropolitan Museum of Art’s mission is to ‘…collect, study, conserve, and present significant works of art across all times and cultures in order to connect people to creativity, knowledge, and ideas.’
“Moments such as this provide an opportunity for conversation, and visual art is one of the most significant means we have for reflecting on both the past and the present, and encouraging the continuing evolution of existing culture through informed discussion and respect for creative expression.”
According to the Met’s description of the work, it depicts Balthus’s neighbor Thérèse Blanchard, who was about 12 or 13 at the time.