The duchess donned a new off-the-shoulder fitted tweed dress by Erdem that featured a deep purple belt, button detailing and a flared skirt.
Kate returned to royal duty last week after being on maternity leave since the birth of Prince Louis in April.
The event marks the first time she has visited the museum in an official capacity since becoming its first Royal Patron in March.
The 36-year-old royal toured the opening display, entitled “Collecting Photography: From Daguerreotype to Digital,” and took in some of the historical prints and contemporary photography the center is showcasing. She also met with curators during her visit.