JK's spokesman said it looked like the books had been stolen from the printers.
Suffolk Police are looking into the possible theft.
The man who found them realised what he had discovered and telephoned the newspaper straight away.
He told them: "I wondered what it was and bent down to pick it up. I was astonished when I read the first page and saw it was the latest Harry Potter book."
The copies had no covers on them, but on the first page of each copy was the title and JK's name.
They were dedicated to JK's husband and her two children. The dedication said: "To Neil, David and Jessica who make my world magical."