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 exhibition tracing the career of the fashion maverick is to arrive in Paris in April 2015.
She succeeds Marie Lannelongue, who has headed the magazine since its launch in France in 2004.
Guests including Tom Ford, Sarah Burton, Mario Testino and Amanda Wakeley crowded into The Wolseley on London’s Piccadilly on Thursday.