Canadian-Egyptian Mohamed Fahmy, one of three reporters with the Qatari broadcaster detained and sentenced to up to 10 years in prison, also needs treatment for Hepatitis C, his lawyers said.
The journalists -- including Australian Peter Greste and the Egyptian Baher Mohamed -- were convicted of aiding the blacklisted Muslim Brotherhood and falsely portraying Egypt as being in a state of "civil war." They have been detained since December 2013.
A court will hear their appeal on January 1, in a case that has sparked an international outcry with US President Barack Obama leading calls for their release.
"Mr Fahmy's detention has become a great danger to his health," his lawyers, London-based lawyers Amal Clooney and Mark Wassouf, said in a statement.
"The authorities should grant him temporary release so that he can receive the medical treatment that he so urgently needs," the statement said.
Signup to our newsletter and follow us on Facebook and Twitter!
Fahmy broke his shoulder before his arrest.
His lawyers say he "suffered a permanent disability in his right shoulder due to an injury exacerbated during his detention" and would need "complicated correctional bone surgeries that also require extensive recovery and support not readily available in prison."
Greste and Fahmy were sentenced to seven years, and Mohamed was jailed for 10 years.
Eleven other defendants tried in absentia, including one Dutch and two British journalists, were given 10-year sentences.
Four other defendants were given seven-year terms, and two were acquitted.
The trial came against the backdrop of strained ties between Egypt and Qatar, which supports the Muslim Brotherhood movement of Mohamed Morsi, the president overthrown by the military last year.