Lewis Jones, a family friend, says the 97-year-old died in his sleep Sunday.
Murray was a close friend of "Invisible Man" novelist Ralph Ellison and wrote widely about American culture. He influenced numerous writers and musicians and helped Wynton Marsalis and others stage the acclaimed Jazz at Lincoln Center concerts.
Duke Ellington called him "the unsquarest man I know." Murray often wrote and spoke in a jazzy, mock-professorial style, not unlike Ellington's stylized stage introductions. Millions of television viewers came to know Murray as a featured commentator in Ken Burns' documentary series "Jazz."