The deaths occurred in Cairo, Menya in Upper Egypt and Damietta in the Nile River delta, the ministry said.
Friday's protests were a response to the military government's Wednesday declaration designating the Brotherhood as a terrorist group, and clashes between loyalists of deposed president Mohamed Morsi and police broke out across the country, Ahram Online reported.
In Cairo, Egyptian police limited a student protest to the campus of Azhar University, one day after a student was killed there. Students threw rocks at police who were deployed to keep them from protesting in the streets.
Students at the university in the Nasr City neighborhood threw rocks and police responded with tear gas and rubber bullets, keeping the students in the area around their dormitories, Ahram Online said.
Demonstrators stopped traffic on the Cairo Circular Highway and burned a police vehicle in Haram. The Interior Ministry said three police vehicles were torched across Egypt, and four soldiers were injured in clashes with demonstrators in Giza, where protesters blocked a road until they were dispersed with tear gas.