Sotheby's France brought the hammer down on a new market-shattering figure for Peinture 162 x 130 cm, 14 Avril 1962 which had been part of late US gallery-owner Sam Kootz' personal collection.
Soulages is one of the best known French contemporary artists, and his work hung in Kootz' gallery along with those by Mark Rothko, Willem de Kooning and Robert Motherwell.
The painting, basically broad horizontal swathes of black, Soulages trade-mark colour, with luminous blue, reached more than double its estimate of between two and three millions euros.
Soulages, from Rodez in the Aveyron Department of central France, had said last year that he would stop using black in his paintings because it was depressing.
The sale exceeded Soulages' Peinture, 21 novembre 1959, Painting 21st November 1959 which received a record-breaking bid of 5.1 millions euros in 2013 at Sotheby's in London.
Meanwhile, as one of its 40th anniversary events, the Pompidou Centre in Paris is lending the Soulages Museum in the artist's native town nine of his major works from 7 June to 5 November 2017.
The paintings will be hung in the musuem's main exhibition space among his other works.
The Pompidou Centre's collection includes some of his paintings from 1948 to 2002, from the Outrenoir (Beyond Black) series such as his works on tar which are being lent by the Pompidou Centre for the first time ever.