In reference to the museum’s decision, the Met’s chief communications officer, Ken Weine, said, “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.”

The petition’s author, Mia Merrill, suggested that the painting be replaced by a painting by a female painter from the same time period as Balthus, who died in 2001.

Ms. Merrill also insisted she was not trying to encourage censorship. “But the blatant objectification and sexualization of a child is where I draw the line,” Ms. Merrill said by phone on Friday.

“Thérèse Dreaming” is not the only painting by Balthus, born Balthasar Klossowski, that portrays girls and adolescents in a controversial manner. “Girl with Cat,” which is on view at the Art Institute of Chicago, uses the same subject and pose as “Thérèse Dreaming,” while his painting “Young Girl in a White Shirt” shows a teenager with her breasts exposed.

Ms. Merrill said that she was not creating petitions to remove any other paintings by Balthus nor was she planning, at the moment, to protest any other works.