The Minneapolis Institute of Art has just selected Katherine Crawford Luber as its next director and president, succeeding Kaywin Feldman who became director of the National Gallery of Art in Washington, D.C., last spring.

Dr. Luber, who headed the San Antonio Museum of Art for the last eight years, will join a small number of women leading museums with budgets of $20 million and higher. She will assume the position in January at the encyclopedic Minneapolis museum, recognized internationally for its Asian art collection.

While female museum directors have achieved parity across the field, according to current statistics provided by the Association of Art Museum Directors, a gender gap persists at the largest museums. Women currently head just 10 of 42 institutions in North America with budgets of more than $20 million. (Ms. Feldman is the first female director in the National Gallery of Art’s 77-year history.)

A native of Texas, Dr. Luber, 58, came to her post in San Antonio with both art historical and entrepreneurial credentials. She worked at the Metropolitan Museum of Art and the Philadelphia Museum of Art after receiving her Ph.D. in 1992 from Bryn Mawr, focusing on the paintings of Albrecht Dürer. She also founded, ran and sold a successful spice company after completing her M.B.A. at Johns Hopkins in 2006.