Police said at least 60 people were injured, two of whom were in critical condition, the Los Angeles Times reported.
The Copts were staging a sit-in outside a state television studio to protest mounting violence directed at them. A week ago, Muslim-Christian fighting killed 15 people.
In this weekend's violence, witness George Thabet told the Times he saw young men throw Molotov cocktails from a bridge into the crowd as others on the ground threw rocks at the sit-in.
The inter-religious conflict has escalated since President Hosni Mubarak was ousted in February by demonstrators calling for democratic reform. He was replaced by an interim military government, which promised Copts it would reopen about 50 churches closed under Mubarak's rule.
Political analyst Ammar Ali Hassan told the Times he sees the religious fighting as political opportunism.
"We still have many people who belonged to Mubarak's regime and it's in their best interest to trigger conflicts like these and keep them alive," Hassan said.