Abercrombie is aging its models to show it is no longer a "teen" brand; company reported a Q2 loss.
Through her Instagram account, Barbie “produces” sponsored content.
The exhibit next spring would be only the second the Met has devoted to a living designer.
The brand has launched an e-commerce site with plans to open its first store in Los Angeles in April, followed by a shop in New York in the summer.
The singer and underwear model was joined by Korean pop star Jay Park as well as fellow Calvin Klein face Kendall Jenner.
The collaboration with Swedish firm Teenage Engineering is the H&M-owned brand’s first outside ready-to-wear.