They said the body of James Henry, 55, who told authorities he was a "retired officer", was found at noon at Ismailiya Awal police station.
The US embassy in Cairo confirmed "that a US citizen prisoner in Ismailiya died from an apparent suicide".
"The embassy is in contact with authorities regarding the case and continues to provide all consular services," an embassy official told AFP.
A report from the prosecutor's office, forwarded to journalists by the foreign ministry, said Henry had hanged himself with a shoelace and a belt.
Egyptian officials had said on August 28 that police arrested Henry in the possession of "maps of the borders in Sinai" and "historical documents".
They said he was detained for violating a curfew imposed because of the latest wave of political unrest sweeping the country.
Henry was stopped on the road between El-Arish and Rafah in North Sinai and told authorities he was on his way to the neighbouring Gaza Strip.
Officials told AFP that a US embassy delegation had visited Henry in his cell last week.
Henry was the second known foreigner to die in an Egyptian prison since a popular military coup overthrew president Mohamed Morsi in July, leading to a state of emergency and a curfew to deal with an Islamist backlash.
In September, a French citizen was beaten to death by cellmates in a Cairo jail. He had apparently been arrested at a checkpoint.
