The winners received one million kronor ($156,385) each.
The Royal Swedish Academy of Music honoured Fleming “in recognition of her sublime unparalleled voice and unique stylistic versatility.”
“Connoisseurs and the general public alike have been dazzled by the beauty of her soft and natural voice, which is equally supple in every register and exudes sensitivity in every tone,” it said.
Nick Mason and Roger Waters accepted the award on behalf of Pink Floyd, selected “for their monumental contribution over the decades to the fusion of art and music in the development of popular culture.”
“Through extensive sonic experimentation, they captured the mood and spirit of a whole generation in their reflections and attitudes,” the academy said.
The Polar Music Prize was founded in 1989 by the late Stig Anderson, the publisher, lyricist and manager of iconic Swedish pop group ABBA.
The prize has been awarded since 1992, when it went to ex-Beatle Paul McCartney.
Among other winners are Brazilian musician Gilberto Gil and German baritone Dietrich Fischer-Dieskau, American jazz musician Dizzy Gillespie, Russian cellist Mstislav Rostropovitch, British pop musician Elton John, French classical conductor and composer Pierre Boulez, jazz pianist Keith Jarrett, US musician B.B. King, British rock legends Led Zeppelin and American popular and folk musicians Bruce Springsteen, Quincy Jones, Stevie Wonder and Bob Dylan.
Last year the prize was shared by US composer Steve Reich and jazz saxophonist Sonny Rollins.