"The prisoner died on his way to the hospital," Nasser Judeh, the Jordanian government spokesman said on Thursday. He identified the dead prisoner as Khalid Fawzi Ali al-Bishtawi.
Judeh told The Associated Press that several police officers suffered "light to medium injuries" during the clashes on Thursday that lasted several hours before police took control of Qafqafa jail about 80km north of the capital, Amman.
Qafqafa holds 34 Islamist prisoners and is one of six such prisons in Jordan.
"A couple of injuries were also reported among the inmates," Judeh said.
It was the second outbreak of unrest at a Jordanian prison in a month.
Ealier reports said security forces had stormed the prison after inmates revolted.
One of the inmates spoke to Aljazeera by mobile phone from inside the prison and said the prisoners were holding two police officers.
"Those officers belong to the so-called terrorism combat forces - they are American agents and friends of Israel," said the caller, identifying himself as Abu Muhammad al-Tahhawi. "They want to humiliate Arabs and Muslims while we are nothing but fighters for the dignity of the Muslim nation."
He identified the two captured officers as Salem Husni al-Jaarat and Owda Muhamad Riaq.
Al-Tahhawi said the prison was besieged and police forces used tear gas.
Al-Tahhawi is serving three years in jail for planning attacks against the American and Israeli embassies in Jordan in 2004.
The spokeman for the Jordanian security forces, Major Bashir al-Daja, denied al-Tahhawi's claim, telling Aljazeera.net's correspondent in Amman, Muhamad al-Najjar: "There was no confrontation. All that happened was a routine inspection to make sure that the prisoners hold no banned items."