The 1921 painting, "Trois Femmes a la Table Rouge," which carried a pre-sale estimate of up to $7 million, was purchased by an unidentified buyer at Sotheby's Impressionist and Modern Art sale in New York, according to the auction house's website.
The pop singer said in April that she bought the painting in 1990 and that selling it would combine her passions for art and education by raising funds for the Ray of Light Foundation, a non-profit organization offering vocational training for street children and poor farmers.
"I cannot accept a world where women or girls are wounded, shot or killed for either going to school or teaching in girls' schools. We don't have time to be complacent," Madonna said in a statement last month.
"I want to trade something valuable for something invaluable - Educating Girls!"
Madonna has adopted two children from Malawi in southern Africa and plans to build 10 schools there.