The clashes broke out outside a police station in the Shubra el-Kheima district when relatives and neighbors of the dead man gathered and then attacked the police with guns and Molotov cocktails, a security source said.
Four of the attackers were killed in clashes, taking to five the total number of people dead, according to a ministry of health, which added 12 others were also wounded, including two policemen and a soldier.
Clashes between police and people have increased in Egypt since the uprising that toppled former president Hosni Mubarak in early 2011.
The army has been called in frequently to restore law and order given police have been widely discredited during security operations.
Clashes also broke out on Sunday, for the second day, at a court in Egypt's second city of Alexandria between protesters and security forces, media reported.
The protesters are demanding worthy verdicts for security officials on trial in the northern city for a deadly crackdown during the Arab Spring uprising two years ago.