Written to the interior ministry in 1895, a month after Dreyfus was sentenced for treason, the letter is expected to fetch between €100,000 and €150,000 ($130,000 and $190,000) when it goes on auction at Sotheby's on Wednesday.
But the sale does not have the support of the Dreyfus family, who say the letter should be donated to a museum or a library instead.
"We urge the seller of this letter to give up this sale," Dreyfus' grandson Charles Dreyfus and historian Vincent Duclert wrote in an open letter seen by AFP.
The men said Dreyfus's historic documents should not "become objects of speculation" and called on the collector to make a "moral gesture" by donating the note to a public institution.
Dreyfus (1859-1935) – a 35 year-old Jew from the Alsace region of eastern France which was at the time occupied by Germany – was found guilty in 1894 of passing secret information to the German military attaché in Paris and sentenced to life imprisonment at the infamous Devil's Island penal colony.
In 1898 the writer Emile Zola published his famous "J'accuse" letter to the president of the day naming officials who framed Dreyfus, and the next year he was brought back for a second trial and then officially pardoned – though not cleared of the charges.
In his prison letter, Dreyfus proclaims his innocence: "I have been sentenced for the most infamous crime a soldier can commit and I am innocent... I ask you, minister, not for grace or pity, but simply for justice."