The women performed a zumba-style routine of spins, funky steps and arm swings to "Pope is Pop", a song written about the pontiff by Italian Igor Nogarotto.
"Tonight you are not alone, Francis is there everywhere, hallelujah, hallelujah," the song blasted from speakers at Rome's Rebibbia prison as the prisoners danced.
After writing the song, Nogarotto and choreographer Alessandra Abbattista decided in April to stage "Pope is Pop" flashmobs around the Italian capital with people from different nationalities and religious backgrounds dancing in homage to Francis.
"I am not religious," said Nogarotto, "but this pope has an amazing charisma. He is humble and close to the people and he doesn't conform to stereotype."
The pope visited the Rebibbia prison in April, washing and kissing the feet of 12 inmates.
For the women who took part, the flashmob was a welcome change from the routine of prison life.
"It gives us hope, hope that we will get through this awful period of our lives and be able to go back and see our families again," said Gisele, an inmate from Brazil.
"When we are dancing we feel a little bit of freedom and an incentive to get through this."