Ahmet Suphi Altındöken was jailed for life without parole in December 2015 for killing and attempting to rape 20-year-old Özgecan Aslan. Altındöken was shot close to his heart and a 6.35mm pistol was used, according to Doğan news agency.
The 27-year-old was taken to hospital to receive treatment after the attack on his life, but medical teams were not able to save him.
Altındöken's father, Necmettin, 51 – who was one of two men jailed as accomplices – was also shot. "We received the information that the person was badly wounded and then died. And we were made aware that the father was also wounded but his life not in danger," government spokesman Numan Kurtulmus said after a cabinet meeting.
"To kill anyone in prison - whoever it is - is unacceptable. Whatever negligence there has been will be brought to light."
Aslan's mother Songul responded to the prison attack by saying: "I don't know what happened. Nothing can bring my daughter back. We do not want to talk about this issue," she told the Hurriyet Daily News.
During the trial it was revealed that Aslan had been travelling on Altindoken's minibus, and when she was the last passenger on the vehicle, he drove to a wood and attempted to rape her. The student defended herself using pepper spray but Altindoken then bludgeoned and stabbed her to death.
Altindoken's father and friend were found guilty of helping him burn and dispose of the body. Aslan's remains were found by police and the three were arrested.
Lawyers said after the trial that it was public pressure with nationwide protests that assisted in the three men receiving aggravated life sentences which is the highest punishment in Turkey after it abolished the death penalty in 2002.
President Recep Tayyip Erdogan said the guilty men deserved "the most severe punishment" after Aslan's killing. Previously, the Turkish president infuriated feminists with his comments last year saying that women were not equal to men.