Archbishop Franco said that in his letter he advised the Holocaust museum he "would not feel comfortable going to Yad Vashem" unless the wording was amended or the photo removed.
Yad Vashem in Jerusalem hosts Israel's annual state ceremony to mark Holocaust Martyrs' and Heroes' Remembrance Day, which will take place on Sunday.
In a statement, Yad Vashem said it was "shocked and disappointed" that the envoy would not partake in the official ceremony, normally attended by Israeli officials and foreign ambassadors to Israel.
The caption also says that "when he was elected Pope in 1939, he shelved a letter against racism and anti-Semitism that his predecessor had prepared.
The caption said Pius XII did, however, protest the treatment of Jews in Hungary and Slovakia towards the end of the war.
Yad Vashem said it had told the Vatican's representative "it was willing to continue examining the issue".
Defenders of Pope Pius XII have said he did everything possible to help Jews, while critics have portrayed him as an anti-Semite and Germanophile whose views were formed while working in Germany before his election as Pope in 1939.
Historians have called on the Vatican to fully open archives on Pius XII papacy, which ended in 1958.