“The Dutch red barn is part of the iconography of America,” she said. “That was part of my initial idea, to raise a barn on the roof.”

Ms. Parker said she gave thought to the people who most use the Met’s outdoor space, where cocktails are served.

“It’s not a fine-art audience — people are coming for the view,” she said. “I wanted to add another ingredient to the view.”

The primary materials in Ms. Parker’s piece all came from a single farm building that was once scheduled for demolition in the upstate New York town of Schoharie — but no barns were harmed in the making of this project.

“We got the bits they didn’t want,” said Ms. Parker, whose work is in museums around the world.

She has made a career out of taking pieces of material and elaborately combining them in surprising ways — less of a deconstructionist than a reconstructionist. And although she calls herself a sculptor, her works fit the installation-art mode that has become a popular feature of museums, galleries and art fairs.