The pope added that the harrowing image which shows a boy carrying his dead brother on his shoulders while waiting in line at a crematorium should be captioned "the fruit of war", accompanied by his signature.
The cards issued by Francis will carry his own signature along with a caption: "The young boy's sadness is expressed only in his gesture of biting his lips which are oozing blood", The Independent newspaper in the United Kingdom reported.
Pope Francis has previously condemned the nuclear weapons and highlighted the plight of children in war zones. After the bombs were dropped on Hiroshima and Nagasaki in 1945, O'Donnell was assigned to document the scenes.
Smoke billows over the Japanese city of Nagasaki after an atomic bomb was dropped on the city
The Catholic church designates January 1 as World Peace Day, and in his comments after Mass to the crowd in the square outside the basilica, Francis noted that this year's focus of the day was the search for peace by migrants and refugees.
Pope Francis described migrants and refugees as the world's "weakest and most needy" in his traditional New Year's address in St. Peter's Square at the Vatican.
Pope Francis said it is important that everyone, including individuals, governments, schools, churches and church agencies, make a commitment to "ensuring refugees, migrants - everyone - a future of peace".
Pope Francis began the New Year praying the world would demonstrate a marked increase in solidarity and welcome for migrants and refugees.
"To call Mary the mother of God reminds us", he said, that "God is close to humanity, even as a child is close to the mother who bears him in her womb".
"Let us not supress hope in their hearts; let us not stifle their expectations of peace! May the Lord grant us to work in this new year with generosity, generosity, to create a more supportive and welcoming world".
He has also spoken out about the threat of nuclear weapons as tensions between North Korea, the USA and its allies remain tense.
Pope Francis has made migrants and refugees a central theme of his papacy in opposition to the negative sentiment against migrants around the world.