In her letter, Mrs Lisbona, who has two teenage daughters with her current husband after 19 years of marriage, said she was worried that if she did take Communion she would be "violating Church rules".
The Pope, who since being elected 13 months ago has established a reputation for phoning ordinary Catholics out of the blue in response to letters they have sent, called her at her home in the central region of Santa Fe on Easter Monday.
He reportedly told her: "A divorcee who takes communion is not doing anything wrong." In a rebuke to the local priest who refused her the Sacrament, he added: "There are some priests who are more papist than the Pope."
When asked whether the remarks attributed to the Pope were correct, a Vatican spokesman told The Daily Telegraph: "We would neither confirm nor deny that - this was a private telephone call made by the Holy Father and we would not divulge the details."
But the reported remarks were in line with the position taken by the Pope in recent months - that the Church should treat divorcees and their partners with more compassion.
The remarks may indicate that the Pope, who has struck a much more inclusive tone than his predecessor, Benedict XVI, on issues ranging from homosexuality to same-sex unions, is testing the water with the intention of changing the Church's position.
The surprising exchange was first revealed by Mrs Lisbona's husband, Julio Sabetta, who said he first answered the call from the Pope, before handing the phone to his wife.
Pope Francis waves to the crowd from the balcony of St. Peter's Basilica where he delivered the Urbi et Orbi at the end of the Easter Mass. Photo / AP
"One of the most wonderful things in my life has just happened - receiving a telephone call from none other than Papa Francesco," he wrote on his Facebook page. "We're Catholics, we believe in God, and though we don't go to Mass every Sunday, every evening we thank the Lord for our family and our work," Mr Sabetta, a pastry chef, said.
The phone call came six months after Mrs Lisbona sent her letter to him. Introducing himself as "Father Bergoglio" - his given name is Jorge Mario Bergoglio - the South American pontiff said he was sorry it had taken him so long to make the call. "It is an issue we are discussing in the Vatican, because a divorcee who takes communion is not doing anything wrong," the Pope reportedly said during a conversation lasting 10 minutes.
The Church currently maintains that unless a first marriage is annulled, Catholics who remarry cannot receive Communion because they are essentially living in sin and committing adultery.
Such annulments are often impossible to obtain, or can take years to process, a problem that has left many Catholics feeling rejected by the Church.
In February, the Pope said divorced and separated couples should not be excluded from Church activities, in remarks which also raised speculation that he may one day lift the ban on divorcees receiving Communion. He said priests should "ask themselves how to help [divorced couples], so that they don't feel excluded from the mercy of God, the fraternal love of other Christians, and the Church's concern for their salvation."
He has also called on the Church to re-evaluate the way that priests and bishops can engage with the children of same-sex couples and divorcees, urging them to "consider how to proclaim Jesus Christ to a generation that is changing".