The man, identified only as Obaidullah, made the allegation in a four-page statement dated March 27 but released recently, The Miami Herald reported Sunday.
"While the soldiers conducted their searches, I and other detainees saw U.S. soldiers rifling through the pages of many Korans and handling them roughly. This constitutes desecration," Obaidullah said in the document.
Military officials have repeatedly said there was nothing unusual about the Feb. 6 search at the communal prison compound known as Camp 6.
A week before the affidavit was made, Marine Gen. John Kelly, head of Southern Command, said, "There's absolutely no mishandling of the Koran."
Navy Capt. Robert Durand said longstanding procedures call for only Muslim interpreters at the camp to search the holy books.
Obaidullah has been held by the U.S. military since 2002.
About 100 prisoners were in their ninth day of a hunger strike Sunday, said Army Col. Samuel House, a prison spokesman. Two of the inmates were being force-fed at the prison hospital and 21 others were being fed twice a day through tubes.