The pontiff made the comment in his weekly address in St Peter's Square, in the first of two talks affirming the role of the elderly in the family and society.
He also said that societies which do not love and care for the elderly are deliberately behaving unacceptably, and that the Church must not stand by and allow this to happen.
Recalling when an elderly person told him her children hadn't visited for eight months, Pope Francis said: "Eight months without a visit from her children. Eight months of being abandoned. This is called a mortal sin. Understand?
"An elderly person is not an alien. The elderly person is us. Soon, or many years from now - inevitably anyway - we will be old, even if we don't think about it.
"While we are young we are tempted to ignore old age as if it were an illness to hold at bay.
"But when we become old, especially if we are poor, sick and alone, we experience the failures of a society programmed for efficiency, which consequently ignores the elderly."
"The Church, faithful to the word of God, cannot tolerate such degeneration."
Louise Morse works for the Pilgrim's Friend Society, which provides care and accommodation for the elderly in a Christian environment.
She told Premier's News Hour: "Jesus Himself made it very clear that we are to honour our parents.
"It's when churches stay away that is particularly distressing for us because we cater for Christians mainly and for them, their churches have been an important part of their lives.
"There's so much wrong teaching, even in our churches, towards older people and what we're saying is older people are not a generation apart - they're part of us. God didn't make a mistake with old age, it's part of His design, part of His plan.
"It's a time when we cascade down experience... especially spiritual experience, because older people have been through the deep waters, and they've been through the fiery trials, and they can tell how God brought them through.
"We need to reassess our values, and reassess: where are we with God in this?"
Listen to Louise Morse speaking to Premier's Des Busteed:
