The famous canvas is considered by experts as representative of the artist at an important juncture in his creative development.
The 1932 painting bought by an unnamed private collector features an image of Picasso's mistress, Marie Therese Walter, in a white bust on a table.
The famous canvas is considered by experts as representative of the artist at an important juncture in his creative development.
Christie's had estimated its value between $25 million and $30 million.
It is expected to be the most expensive sale of the season, when the three major fine-art auction houses, Sotheby's, Christie's and Phillips, are auctioning works worth an estimated $300m.
Christie's spring-time auctions began this week with a sale of impressionist art.
On Wednesday, Christie's main competitor, Sotheby's, will offer Picasso's "Guitar and Fruit Bowl", painted in 1932 and expected to fetch between $10m-$15m.
Art historians say the work is also a disguised portrait of Marie Therese Walter, who was for 10 years the mistress of the Spanish painter.
Muse
Marie Therese was portraited by Picasso in several of his works.
It is not clear exactly when they first met.
In the mid-1920s Picasso walked past Galeries Lafayette in Paris and stopped in front of her, when she was only about 15 years old.
"Mademoiselle, you have an interesting face. I would like to paint your portrait. We are going to do some extraordinary things together," he said to her, according to John Richardson's biography Through the Eye of Picasso.
He received permission from her mother for her to pose for a painting and they became lovers.
This week's auctions are the first since the US Government launched an investigation in January into allegations that Sotheby's and Christie's conspired to fix commissions.