A senior Vatican official on Friday said the purpose of the meeting was to restart dialogue with the Islamic world.
Invitations were sent for the meeting on Monday at the pope's summer palace in Castelgandolfo, outside Rome.
Muslim diplomats accredited to the Holy See hoped it would help to restore trust between the Roman Catholic Church and Muslims offended by the pope's speech last week in his native Germany.
Ahmad Faihma, Iran's deputy ambassador to the Holy See, said: "We welcome it and are definitely going to participate.
"This is a positive signal from the Vatican. I know that this will improve relations with the Islamic world."
Fathi Abuabed, head of international relations at the Arab League's Vatican mission, said: "This meeting will be very important, especially in these days, to try to stop every action that is not good."
The leader of more than one billion Roman Catholics has expressed regret three times in the past week for the reaction caused by his speech quoting the 14th-century Byzantine Emperor Manuel II Palaeologus, who spoke of Prophet Muhammad as bringing nothing but evil to humanity because of his "command to spread by the sword the faith he preached".
He has stopped short of the unequivocal apology requested by many Muslims.
The pope said to his Wednesday audience his intention had been to "explain that religion and violence do not go together but religion and reason do".
Many Islamic organisations, including the Muslim Brotherhood in Egypt, want the pope to apologise for the anti-Islam remarks that came in his speech and explain in detail what his views on Islam are.