The global human rights organisation is also accusing authorities of failing to prosecute those responsible for a surge in kidnappings and assassinations by armed groups during the last three years.
Najia Bounaim, at Amnesty International's regional office in Tunis, said: "The Egyptian authorities have consistently failed to protect Coptic residents of North Sinai from a longstanding pattern of violent attacks, they must not let them down further now."
"The government must also end the prevailing impunity for attacks against Christians elsewhere around the country and end its reliance on customary reconciliation deals which further fuel a cycle of violence against Christian communities."
While attacks against Coptic Christians in Egypt have decreased since former President Mohamed Morsi was ousted in a military coup in 2013, at least seven murders of believers since 30th January this year indicate a recent spike in violence.
Around 150 Coptic Christian families had fled the area of al-Arish, with most heading to the neighbouring governorate of Ismailia, according to the Egyptian Minister of Parliamentary Affairs.
Najia Bounaim went on to say: "This terrifying wave of attacks has seen Coptic Christians in North Sinai hunted down and murdered by armed groups.
"No one should face discrimination - let alone violent and deadly attacks - because of their religious beliefs."
Amnesty International suggested state-sponsored reconciliation agreements have not solved the problem but have, in some cases, seen Christians evicted from their homes.
The organisation fears those fleeing to Ismailia are living in overcrowded temporary accomodation where they lack essential services.
Najia Bounaim added: "The government has a clear duty to ensure safe access to housing, food, water and medical and other essential services to all those who have been forced to leave their homes due to violence and persecution."