The musician's sons say he died Thursday but did not release details. Anderson suffered a heart attack earlier this month.
Fred Anderson was well-known for his smooth, velvety playing style. His nightclub, The Velvet Lounge, is known as one of the cradles of contemporary jazz.
Anderson performed in relative obscurity until the 1990's when he became a regular on the jazz-festival circuit in the United States and Europe.
Funeral arrangements are pending.