It was written during the contentious debate over the document's ratification. A private collector offered it for sale at Christie's on Friday.
Christie's says the seven-page letter was purchased by an anonymous phone bidder for $1,443,750. Bidding was between the phone bidder and a woman in the room.
Dated April 25, 1788, it is addressed to Revolutionary War Officer John Armstrong.
Washington writes that he doubts "whether the opposition of the Constitution will not ultimately be productive of more good than evil."
He also says the framers of the Constitution "have given the rights of man a full and fair discussion."