The British-born archbishop, 68, had been the president of the Pontifical Council for Interreligious Dialogue since 2002.
His appointment takes place at a time of acute international tension in the wake of the publication of cartoons of Mohammed in Western newspapers.
The first Vatican delegate to the League of Arab States, an alliance established in Cairo in 1945, was appointed in 2000 by Pope John Paul II.
In December 1991 he was appointed secretary of that council and ordained bishop the next month.
Born in Walsall, England, Michael Fitzgerald entered the Congregation of the Missionaries of Africa, the “White Fathers,” and was ordained a priest in February 1961.
In the last few years, Archbishop Fitzgerald has presided over the Committee of Islamic-Catholic Dialogue together with the Al-Azhar Permanent Committee for Dialogue with the Monotheist Religions, publishing joint appeals for peace among members of various religions.