The young woman was brought to one of the Polish pontiff's weekly audiences in St Peter's Square in 2000 and started screaming, writhing on the floor and drooling.
The encounter is described in a new book by Father Gabriele Amorth, the exorcist for the diocese of Rome.
As soon as she entered St Peter's Square, in front of the Vatican, her behaviour became bizarre.
"When John Paul appeared, she began to wail. Ten people had to hold her down. She wanted to fling herself at the Pope. Her face was full of hate. She was drooling, uttering blasphemies.
"Her body trembled. She was like a beast ready to attack," Father Amorth wrote in his book, The Last Exorcist – My Fight Against Satan, which was released on Tuesday.
After the audience was over, the Pope reportedly asked to be taken to see the woman in his Popemobile.
"Sabrina was in a trance. Her eyes were two white orbs. She was drooling and throwing her head backwards. As soon as she was brought close to the Pope she started yelling 'No, leave me alone!' The pope carried out an exorcism on the spot. He blessed her several times. And then he left," wrote Father Amorth, the founder and president of the International Association of Exorcists.
But the exorcism did not work – when Sabrina was brought to see Father Amorth later that day, she was still possessed, according to Father Amorth.
"She was very agitated. I started to exorcise her. But the Devil wanted to show that he was still in command. I started to pray and said 'Get out, foul spirit.' It replied 'You get out, priest'. I said 'Why are you in this woman? Answer in the name of Christ'. The spirit answered 'You must all worship me because I am the strongest. I am God.'"
Father Amorth claimed that the young woman then got up from her chair and proceeded to walk up the wall behind him "as if it was the most natural thing in the world. She walked against every law of gravity."
It eventually took many sessions to cleanse her entirely of her demons, he said. "But I'm convinced that in some way the exorcism carried out by JPII left a trace in her."
The Pope had more success with an exorcism in the Vatican in March, 1982, when a young girl named Francesca Fabrizi was brought to him by the Bishop of Spoleto in Umbria.
"She was writhing around on the floor, crying out. She became calm when the Pope said 'Tomorrow I will say mass for you'," Father Amorth wrote. She went on to live a normal life, getting married and having children.
In his book, he also claimed the current Pope, Benedict XVI, performed an exorcism on two men possessed by the Devil at one of his weekly audiences in St Peter's Square in May 2009.