Six of the dead were from the same family, and another 18 people, including children, were wounded, the Coptic Church's spokesman said in a statement.
Islamic State claimed responsibility for the ambush in Minya province in central Egypt, the militant group's Amaq news agency said, without providing evidence of its involvement.
Footage posted on social media showed bodies inside a bus with apparent gunshot wounds. Reuters was not able to verify the authenticity of the pictures.
The attackers then fled, a witness at the monastery said.
Local resident Hilal told Reuters he rushed to the scene after hearing about the attack and saw the militants on the road.
"Some of us came to try and block the road. There were three four-wheel drive vehicles and the militants opened fire ... The militants wore white thobes and chequered head-dresses," he told Reuters.
Islamic State and affiliated groups have claimed responsibility for a series of attacks on Christians, including one that killed 28 people in almost the same spot in May 2017 https://www.reuters.com/article/us-egypt-security/he-said-he-was-christian-they-shot-him-says-son-who-saw-father-die-idUSKBN19B176.
Egypt's army and police launched a crackdown on the militant groups in February, targeting the Sinai Peninsula as well southern areas and the border with Libya.
President Abdel Fattah al-Sisi said he mourned the victims as martyrs and vowed to push ahead with the campaign.
"I assert our determination to fight dark terrorism and to pursue the perpetrators," he said on Twitter.
The European Union said it was a "stark reminder of the security challenges that Egypt is facing".
Egypt says fighting Islamist militants is a priority to restore security after the years of turmoil that followed the "Arab Spring" protests in 2011.
The public prosecutor said a team of investigators has been despatched to the scene of the attack to investigate. (Reporting by Mohamed Abdellah and Omar Fahmy; Writing by Nadine Awadalla and Sami Aboudi; editing by John Stonestreet and Andrew Heavens)
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)