The BBC reported the demonstration, which involved people overturning a police van and throwing firebombs, took place in Cairo hours after nearly 1,000 Egyptians set Algerian flags ablaze near the Algerian Embassy.
The protests stemmed from reports that Egyptian fans were attacked after leaving the World Cup qualifying match in Sudan. The incidents prompted Thursday night's flag burnings, which escalated into Friday morning's protest.
The ministry said 11 police officers were among those injured. Fifteen cars were damaged.
Algeria's 1-0 soccer tournament qualifying victory over Egypt Wednesday also prompted harsh words from Alaa Mubarak, son of Egyptian President Hosni Mubarak.
"When you insult my dignity ... I will beat you on the head," the younger Mubarak said regarding Algeria.
The BBC said Algeria earned the last African spot in the 2010 World Cup finals with its victory over Egypt.