The priest, Mina Aboud Sharween, was attacked on Saturday afternoon while walking in the Masaeed area in El Arish.
Five police offers were killed in El Arish on Friday.
Muslim Brotherhood has fiercely criticized Coptic Pope Tawadros, spiritual leader of Egypt's 8 million Christians, for giving his blessing to the removal of the president and attending the announcement by armed forces commander General Abdel Fattah al-Sisi suspending the constitution.
The Muslim Brotherhood’s political wing, the Freedom and Justice Party has called on the supporters of ousted President Mohammed Morsi to continue protests against his ouster.
The Tamarod movement, which spearheaded massive demonstrations against Morsi, and opposition groups have also called on Egyptians to hold rallies on Sunday to defend “the legitimacy of the revolution.”
Morsi was unseated on July 3, and the chief justice of Egypt’s Supreme Constitutional Court, Adly Mansour, was sworn in as interim president of Egypt on July 4.
Morsi is reportedly being held “preventively” by the military. Senior army officials say he might face formal charges over accusations made by his opponents.