Yousef Skaki has been on hunger strike since June 12. He had a heart attack in 2010, suffers from kidney disease and recently had an operation on his retina, the Hebron-based society said.
He was previously held in Israel's Beer Sheva prison. Skaki's daughter visited the prison but Israeli guards refused to allow her to see her father, the group said, adding that she died on April 22.
The society said Skaki was beaten in Ashkelon prison by Nahshon and Metzada units of the Israeli Prison Service despite his critical condition.
On Thursday, a prisoners' rights group reported that the units raided Ashkelon jail, firing tear-gas canisters and beating detainees with batons.
The Palestinian prisoners' society urged the International Red Cross to send a medical delegation to visit Skaki, and said his life was at risk.