The attackers "killed seven people and wounded 14, all of whom are in the Sheikh Fadel hospital in Beni Mazar" about 120 miles south of Cairo, Bishop Makarios of Minya told Agence France-Presse.
The local Islamic State affiliate which spearheads militants fighting security forces in the Sinai Peninsula claimed responsibility for the attack in a statement, according to SITE, a USA -based group that monitors and translates militants' statements.
The Islamic State group claimed the attack in a message via its propaganda agency Amaq. But other attacks carried out by Islamic State (IS, formerly ISIS) have been far more deadly.
The Interior Ministry, which oversees the police, and the security officials said Friday's attackers used secondary dirt roads to reach the buses carrying the pilgrims, who were near the monastery at the time of the attack.
President Abdel Fattah al-Sisi offered his support to the victims in a statement on Twitter. ". I wish speedy recovery of the wounded and confirm our determination to continue our efforts to combat black terrorism and to pursue the perpetrators".
Egypt's prosecutor's office said it had received reports of "gunfire targeting a bus carrying a group of Copts returning from the Monastery of Saint Samuel the Confessor".
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Coptic Christians make up about 10 percent of Egypt's predominantly Sunni Muslim population.
Last month, the Egyptian military sentenced 17 people to death over a series of suicide bombings of churches claimed by IS that left dozens dead.
The government imposed a three-month state of emergency across the country after the April 2017 church bombings.
Coptic Orthodox Church spokesman Boulos Halim said the death toll was likely to rise.
A year earlier, an Isil suicide bomber killed nearly 30 worshippers at a church in Cairo located in the Saint Mark's Cathedral complex, the seat of the Coptic papacy.
Several of the attacks have targeted Christians and churches.