International Christian Concern (ICC) also says the town's only church was partly destroyed with gun-fire and bricks.
It says around twenty armed men arrived in cars to Al-Our last Friday. These men were joined by more than a hundred locals, according to ICC.
They arrived on the same day people from the area was due to celebrate Mass to remember 40 days since Islamic State beheaded 21 Coptic Christians.
According to ICC, the mob fired at Virgin Mary Church with their guns before throwing stones and bricks at it. They also destroyed the church's grounds, sign and windows, and a car which was parked outside the church.
ICC also says the attack was premeditated, because bricks had been delivered to the town beforehand which were then used to throw at the church.
Fr Makka Issar, the priest of Virgin Mary Church, said: "I called the police many times and asked them to come to guard us but they came late and after their arrival they didn't guard the church.
"They stopped in the entrance of the village. Even still they allowed the cars of the attackers to enter the village and attack us and the church without any intervention from them to protect us.
"I charge the responsibility of what happened to the policemen, and I accuse them accuse them of inaction, indifference and complicity."
ICC says the the mob also attacked the family of Samuel Alham Wilson, one of the 21 Coptic martyrs.
His brother, Bebawy Alham Wilson, said: "I was alone in the home with my wife, wives of my brothers, and my mother. My brothers were in the church at this time. The attackers attempted to storm my home, I hurried and locked the door and barred it. They then hurled stones at my home."
Roughly 50% of people in Al-Our are Christians, a much higher percentage than the Egyptian national percentage of just under 13%.