When attacked, the bus was driving along a side road to the monastery because the main road was closed after earlier security orders due to its desert location and lack of phone communication, it added.
Church spokesman Bouls Halim said the death toll in Friday's attack was likely to rise.
Bishop Makarios of Minya said the wounded were taken to a hospital in Beni Mazar, around 200 kilometres (120 miles) south of Cairo.
President Abdel Fattah al-Sisi said he mourned the victims as martyrs and vowed to forge ahead with a campaign against jihadists. The province of Minya has become known for its anti-Christian violence and Egyptian authorities are already being questioned for not securing the route taken by the bus.
Sarah Leah Whitson, Executive Director of the Middle East and North Africa Division of Human Rights Watch, condemned the attack on Twitter. "Condolences to this beleaguered and long-suffering community", wrote HRW's Middle East Director Sarah Leah Whitson.More news: Nintendo and Sony tussle for top-selling console in 2018
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Egypt's Coptic Christian minority, which makes up an estimated 10 percent of the population, has been a frequent target of attacks and persecution since the uprising that toppled former president Hosni Mubarak in 2011.
Egypt's government imposed a three-month countrywide state of emergency after the April 2017 church bombings.
There was no immediate claim of responsibility for the attack.
Just last month, an Egyptian military court handed down death sentences to 17 people convicted in a series of fatal attacks on Christians throughout the country since December 2016.
On Saturday, el-Sissi is to open the World Youth Forum in the Sharm El Sheikh resort in Sinai, which has also seen deadly militant attacks.