The Liebermann painting had been returned to the heirs of its original Jewish owner, David Friedmann, who put it up for sale.
The identity of the buyer has not been revealed.
Sotheby's director Bernhard Brandstaetter said the Gurlitt collection was "probably the most significant find in the last 30 years".
He added: “The challenge is to go through the provenance of every single picture in this collection.
"It is a lengthy process to establish where a picture comes from, when it was bought and so on.
The auction also included a Gustav Klimt portrait which was looted from its Jewish owners by the Nazis.
It sold for £24,789,000, exceeding the pre-sale estimate of £18 million.
