Egypt says fighting Islamist militants is a priority to restore security after the years of turmoil that followed the "Arab Spring" protests.
The Islamic State (IS) killed more than 40 people in twin church bombings in April 2017 and a month later shot dead nearly 30 Christians in Minya province as they headed to a monastery on a bus.
Bishop Makarios of Minya said the wounded had been taken to a hospital in Beni Mazar, around 200 kilometres (120 miles) south of Cairo.
The incident took place on Friday as the vehicle was heading towards the Saint Samuel Coptic Christian monastery near Minya, a city about 270km south of the capital, Cairo.
A security official confirmed the attack, adding that there were "dead and wounded".
The Islamic State group claimed responsibility for that attack. But other attacks carried out by Islamic State (IS, formerly ISIS) have been far more deadly.
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El-Sissi, who has made the economy and security his top priorities since taking office in 2014, wrote on his Twitter account that Friday's attack was created to harm the "nation's solid fabric" and pledged to continue fighting terrorism.
The Islamic State has repeatedly vowed to go after Egypt's Christians as punishment for their support of President Abdel-Fattah el-Sissi.
"I assert our determination to fight dark terrorism and to pursue the perpetrators", he said on Twitter.
Assailants reportedly used side roads to reach the main highway and shoot at the buses, which were nearing the monastery.
The terror group killed more than 40 people in twin church bombings in April 2017 and a month later shot dead 28 Christians in Minya province as they headed to a monastery on a bus.
Coptic Orthodox Church spokesman Boulos Halim said the death toll was likely to rise. The previous attack in May 2017 left almost 30 people dead.