The bus came under attack when it was heading to Anba Samuel monastery in the Minya Governorate, 250km south of Cairo.
The gunmen were riding in three 4x4 vehicles, the Ministry of Interior said.
Twenty-six Christians were killed and 25 others injured in the attack, it said.
Sources and eyewitnesses said that most of the victims were children.
Reports said there had been between eight and 10 attackers who were wearing military uniforms.
No one has claimed responsibility for the attack.
There have been a number of attacks on Copts in the country in recent months claimed by Islamic State (IS) militants.
Two suicide bombings targeting churches in Tanta and Alexandria on April 9 left at least 46 people dead.
In December, an attack on a Coptic church in Cairo killed 25 people.
Coptic Christians, which make up about 10 per cent of Egypt's 91 million population, have faced persecution in Egypt, which has spiked since the toppling of Hosni Mubarak's regime in 2011.
Egypt had imposed a nationwide three-month state of emergency after the April bombings, with the option to extend for another three months.
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