The one-page signed note in German, believed to have been written in July or August 1786, asks Nikolaus Joseph von Jacquin to return three music scores by way of messenger.
"I ask you to send me by the bearer of this, the Quartet in g minor, the Sonata in Eb and the 'New Trio in g,'" it reads.
The pieces referenced are Mozart's Piano Quartet No. 1 in G minor published 1785, Violin Sonata No. 33 in E-flat major from 1785, and Trio for Piano, Violin and Cello in G Major.
Mozart finished the trio on July 8, 1786, suggesting the letter was written shortly afterwards, said Boston-based firm RR Auction.
The firm identified the buyer as "an East Coast music collector," who said it would be the centrepiece of his collection.
"Mozart letters are among the most sought after of all musical autographs," said Bobby Livingston, Executive VP at RR Auction. "This is a truly outstanding example," he added.
Born in Salzburg in 1756, Wolfgang Amadeus Mozart is considered one of history's greatest composers. His wealth of operas, concertos, symphonies and chamber music profoundly shaped classical music. He died in Vienna in 1791 at the age of 35.