The Vatican newspaper l'Osservatore Romano published the new version of the prayer in Latin and said it should be used by the traditionalist minority starting this Good Friday, March 21.
Apart from the deletion of the word "blindness," the new prayer also removes a phrase that asked God to "remove the veil from their hearts".
But the new prayer hopes that Jews will recognise Christ.
Jewish groups had protested against the old prayer and had asked the Pope to change it.
According to an unofficial translation from Latin, the new prayer says in part:
"Let us also pray for the Jews. So that God our Lord enlightens their hearts so that they recognise Jesus Christ saviour of all men."
It also asks God that "all Israel be saved".
Jewish groups complained last year when the Pope issued a decree allowing a wider use of the old-style Latin Mass and a missal, or prayer book, that was phased out after the reforms of the Second Vatican Council, which met from 1962 to 1965.
"It is less offensive in its language but it still is in contradiction to changes that the late Pope John Paul brought about," said Abe Foxman, national director of the Anti Defamation League in the United States.
"John Paul taught that the Jewish people are the older brothers of Catholics and that Judaism has its own merits and viability. The language is better but it's still troubling," he told Reuters by telephone.
Good Friday is the day Christians commemorate Christ's death.
Only some several hundred thousand traditionalists follow the old-style Latin rite and will use the Latin prayer.
The overwhelming number of the world's some 1.1 billion Catholics attend mass in their local languages.
They would use a post-Second Vatican Council missal, which includes a Good Friday prayer for Jews which asks that they "arrive at the fullness of redemption".
Benedict's decree, issued on July 7, authorised wider use of the old Latin missal, a move which traditionalist Catholics had demanded for decades but which Jews and other Christian groups said could set back inter-religious dialogue.
Implementation of the decree has been difficult. The Pope's number two, Cardinal Tarcisio Bertone, said recently the Vatican was preparing a document on how it should be introduced around the world.