The "Portrait of a girl," which portrays a young girl with large, sad eyes, her hands held together as if in prayer, is believed to be an early work by the Sevillian artist best known for his masterpiece "Las Meninas", on display in Madrid's Prado Museum.
It is believed to have been painted by Velazquez around 1616 or 1617, when the artist was only 17 or 18 years old and still living in the southern Spanish city of Seville, the auction house said.
It had been in the same family for several generations but had never been properly analysed until the owner decided to sell it.
Richard de Willermin, a specialist on 17th century Spanish art who collaborates with the auction house, examined the small oil on canvas painting and concluded it was by Velazquez.
Specialists at the Prado Museum have also looked at the painting, but the museum has not commented publicly as it never gives any opinion about works that are not part of its own collection.
The painting's starting price had been €8 million ($8.7 million), Abalarte said, but there was no higher bidding.
The identity of the buyer was not revealed, but the painting is banned from leaving the country by order of the government, which prohibits any work that could be part of Spain's heritage from being taken abroad.
A slow and meticulous worker, Velazquez is thought to have painted fewer than 200 works in his entire career. About 120 survive to this day, roughly half of them in the Prado.