Church spokesman Bouls Halim said the death toll is likely to rise. Local church officials in Minya province put the death toll at 10, but the higher figure could not be confirmed.
No group immediately claimed the attack south of the capital Cairo, which bore the hallmarks of Islamic State militants who have for years been fighting security forces in the Sinai peninsula and along Egypt's porous desert border with Libya.
Archbishop Angaelos, the Coptic Archbishop of London, told Premier: "We pray for the those who continue to plan and perpetrate these attacks because it's only in them seeing the true effects of what they're doing and looking at those who are mourning - that will change their minds."
It is the second attack on pilgrims heading to the St Samuel the Confessor monastery in as many years. The previous attack in May last year left nearly 30 people dead.
PRAYER ALERT: Please pray for our church family in #Egypt, where at least seven Christians have been killed and nine injured in an attack on a bus convoy in Minya today. Armed terrorists opened fire on two buses as they were leaving Saint Samuel's monastery.
— Open Doors UK ن (@OpenDoorsUK) November 2, 2018
The Interior Ministry, which oversees the police, said the attackers used secondary dirt roads to reach the bus carrying the pilgrims, who were near the monastery at the time of the assault.
The attack last year was the latest in a deadly series that targeted churches in Cairo, the Mediterranean city of Alexandria and Tanta in the Nile Delta, north of the capital.
Those attacks, all claimed by IS, left at least 100 people dead and led to tighter security around Christian places of worship and other Church-linked facilities.
Egypt's Christians, who account for 10% of the country's 100 million people, complain of discrimination in the Muslim majority country.
Reports emerging now: At least seven people killed, 14 injured in attack on bus heading toward Coptic monastery in Egypt
— CopticMediaUK (@CopticMediaUK) November 2, 2018
The Church allied itself with President Abdel-Fattah el-Sissi when, as defence minister, he led the 2013 military overthrow of Islamist president Mohammed Morsi.
Click here to listen to Premier's Alex Williams speaking with the Coptic Archbishop of London, Archbishop Angaelos:
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