The buyer wished to remain anonymous, according to auction house Weidler.
The 1914 painting of the city hall in Munich was put up for sale by two elderly sisters, whose grandfather bought the artwork in 1916, when Hitler was in his 20s. The work measures 28 by 22 centimetres (11 inches by 8.7 inches).
As a budding young artist, Hitler applied to the Vienna Academy of Art but was rejected. He continued to paint however, copying images from postcards that he sold to tourists.
Experts consider his work to be of mediocre quality and the larger auction houses generally refuse to sell the late Nazi dictator's works.
Nuremberg famously hosted the trials of Nazi leaders after World War II. Hitler himself committed suicide in his Berlin bunker in the dying days of the war.