The Islamic State group has claimed responsibility for Tuesday's (April 18) attack, the Associated Press reports.
St. Catherine's Monastery, located in a remote desert and mountainous area of the South Sinai governorate, was built in the sixth century at the foot of Mount Sinai. It is a UNESCO world heritage site and a popular destination for tourists and visitors to the Red Sea.
Militants ascended onto an elevated hilltop overlooking the police checkpoint several hundred metres outside the monastery. Then they opened fire.
Some of the gunmen were wounded when police returned fire, Egypt's Interior Ministry said.
The northern Sinai region is under a state of emergency, with near-daily Islamic State militant attacks on police and security forces. The militants are attacking other parts of Egypt and their tactics are believed likely to inflame sectarian tensions and embarrass President Abdel-Fattah el-Sissi.
The Islamic State group has vowed more attacks against Christians in Egypt, the Associated Press says.
Pope Francis will visit the country next week. The attacks have increased fears about security ahead of the visit.
Suicide bombers attacked two Egyptian churches on Palm Sunday, killing 45. The Sinai-based Islamic State affiliate claimed credits for the attacks.
In response, President el-Sissi declared a three-month state of emergency and deployed armed forces to help guard important installations and churches across Egypt.'
(Story from the Catholic News Agency)