Barakat, 64, was killed by a car bomb in Cairo in June 2015. He was the most senior state official assassinated since the toppling in mid-2013 of elected president Mohamed Mursi of the Muslim Brotherhood. There was no claim of responsibility for the attack at the time.
Interior Minister Magdi Abdel Ghaffar told a news conference that the attack was ordered by Turkey-based leaders of Egypt's oldest Islamist movement and coordinated with fellow Islamist group Hamas, which he said provided training and explosives.
Hamas spokesman Sami Abu Zuhri denied the accusations, calling them groundless and incorrect. There was no immediate comment from the Muslim Brotherhood.
Abdel Ghaffar said Egypt had arrested 48 members of a Brotherhood cell aimed at undermining security through a series of attacks. Fourteen of them had confessed to killing Barakat.
He said Yehia Moussa, health ministry spokesman during Mursi's presidency, had planned the operation. Moussa is now living in Turkey.
"This is a very big conspiracy that started a long time ago and continued," he said.
Judges and other senior officials have been targeted by radical Islamists since then-military chief Abdel Fattah al-Sisi ousted Mursi following mass protests against his turbulent rule.
Sisi, who went on to win a presidential election in 2014, banned the Brotherhood and jailed thousands of its followers. Shortly after Sisi took power, security forces killed hundreds of Mursi supporters in a single day in the bloodiest episode in Egypt's modern history.
The Egyptian judiciary says it is independent of the government and military, but some judges have been accused by human rights groups of bias after handing down lengthy jail terms and mass death sentences.
The crackdown, which has included restrictions on freedom of protest, has angered many opponents of Sisi who has struggled to suppress an insurgency that is raging in the eastern Sinai Peninsula, which borders Hamas-controlled Gaza and Israel.
Barakat's assassination cast doubt on Egypt's ability to contain the insurgency, which has seen hundreds of police and soldiers killed since Sisi took over. The Brotherhood has been designated terrorist. The group says it rejects violence.
The most active militant group is Sinai Province, which has pledged allegiance to Islamic State. Egypt makes no distinction, describing such groups as an existential threat.
The interior ministry showed video clips of men, most in their early 20s, confessing to joining protests and later attacking police with fireworks, destroying electricity towers, and going to Gaza for military training from Hamas.
"I received a firearms course, a car bomb course, and a military tactics course. I returned to Egypt three months later and remained in contact with Hamas intelligence officers," one young man told the camera.
"I was later told to prepare for an operation with others where we would assassinate the public prosecutor."
The young men said they planted a car filled with explosives and detonated it remotely the following day as Barakat's motorcade passed by.
"As soon as the motorcade moved (near the car bomb) I pressed the button and we took a photo then moved in a red hatchback car," said another young man.
Authorities have repeatedly paraded on video what they say are militants confessing to violence. It was not immediately possible to verify the authenticity of the confessions.