The officials said on Friday that militants stormed the home of Kamel Youssef, a plumber, the previous day and shot him to death in front of his wife and children in the town of el-Arish.
The killing comes days after Egypt's Islamic State affiliate, which is based in the Sinai Peninsula, vowed to step up attacks against the embattled Christian minority.
The officials spoke on condition of anonymity because they are not authorized to talk to reporters.