Marzio died Thursday night in Houston. Goffe did not release further details.
The MFAH was founded in 1900 and has nearly 63,000 works. Marzio had been director since 1982.
Goffe says Marzio took a special interest in education.
His book, "American Art and Philanthropy: Twenty Years of Collecting at the Museum of Fine Arts, Houston," was published in November.
Another Marzio-involved book, "Masterpieces from The Museum of Fine Arts, Houston: Director's Choice," was published in February, with staff contributions.
His wife, Frances, works as a curator at the museum.
Learn more about Marzio's influence on the Museum District on CultureMap.com