The pontiff had hosted the grand imam, Ahmed al-Tayeb, at the Vatican last May, in a landmark meeting with one of Islam's top clerics.
That encounter was the culmination of a steady improvement in a relationship that had broken down because of a series of spats under Francis's predecessor Benedict XVI.
The current pope has made interfaith dialogue and reconciliation a leading theme of his pontificate and has also overseen an improvement in relations with the Orthodox and Protestant wings of Christianity.
The Argentine pope has a long-standing invitation to visit Egypt from its president.
The Vatican said the pope was going also upon invitations from Catholic bishops in Egypt, Coptic Orthodox church leader Pope Tawadros II and the grand imam of the Al-Azhar mosque, Sheik Ahmed el-Tayyib.
Last month, the Vatican’s point man on Muslim relations, Cardinal Jean-Louis Tauran, participated in a conference at Al-Azhar focused on how Muslim and Catholic leaders can work to counter fanaticism, extremism and violence in the name of religion.
Pope Francis has stressed working for reconciliation and overcoming divisions among all peoples as urgent goals of his four-year-old papacy.
In contrast, Vatican relations with much of the Muslim world suffered early in Benedict’s papacy, when, during a speech in 2006 in his native Germany, he spoke about Islam’s relation to violence.
Most of Egypt’s Christians are members of the Orthodox church led by Tawadros. Christians overall are believed to account for about 10 percent of the country’s 92 million people.
Christians often complain of discrimination, citing their apparent exclusion from top positions in the security services, academia and the diplomatic service.
Egypt's government has recently sought to reassure Egypt’s Christians, promising them equality and protection.
But a series of brutal killings of Christians recently in northern Sinai claimed by a local affiliate of the Islamic State has forced hundreds of Christians to flee the area in search of safety elsewhere in Egypt.