Most of the folks in the "Arab Republic of Egypt" (that is the English translation of the country's name, you know), formerly known as the "United Arab Republic" are, big surprise, Arabs. But don't let the facts get in your way. Read more here: http://www.cia.gov/cia/publications/factbook/geos/eg.html
Correction noted, Hotshot.
Still, there are plenty of Muslim terrorists and Islamic extremists who are not Arabic. To assume so would be to say that Arabs are the only ethnic group in the Middle East (which they are not).