The work is a 1964 reworking of one first made in 1919 when Duchamp bought a postcard of Da Vinci's famous work and drew the genderbending facial hair on it.
He called it LHOOQ, which can be read as the English "Look" or in French as "Elle a chaud au cul", roughly translatable as "She's horny".
Duchamp is regarded as one of the fathers of conceptual art, particularly because of his readymades - everyday objects that he declared to be artworks, most famously a urinal that he turned on its side and called Fountain.
LHOOQ is a rectified readymade, in that Duchamp actually altered it, however minimally.
Its presale estimated price was 400,000 to 600,000 euros.
Record for Swiss surrealist
Other works in the sale of the collection of American Arthur Brandt also sold for more than their estimates.
Duchamp's Boîte-en-valise (Box in a Suitcase), a portable museum of reproduced or miniature versions of 68 of his works, wold for 319,500 euros, having been estimated at 180,000 to 250,00 euros.
Seven versions were made between 1941 and 1966.
Buste d'homme by Swiss artist Kurt Seligmann, a less well-known surrealist than Duchamp, was estimated at 60,000 to 80,00 euros but sold for 181,250 euros, a record for the artist, according to Sotheby's, Paris, where the auction took place.
Six pieces by American artist and photographer were up for sale.
One, The Lovers, had been estimated at up to 25,000 euros but fetched 81,250 euros.
The Mona Lisa featured in a legal case in Paris this week.
Performance artist Déborah de Robertis was declared not guilty of indecent exposure after posing in front of da Vinci's work in crutchless trousers because the court found she had been executing a "militant and artistic act", the court found.