Children, some dressed in school uniforms, threw stones and made obscene gestures at security officers, Ahram Online reported.
Molotov cocktails were hurled at security officers on Qasr el-Aini Street, the Egyptian Interior Ministry said.
A journalist at the scene reported tear gas was fired at demonstrators near the Shura Council and a number of passersby suffered gas inhalation.
Human rights activists and lawyers said police arrested a number of demonstrators in Tahrir Square early Tuesday.
Demonstrations began Monday marking the one-year anniversary of last year's clashes on Mohamed Mahmoud Street where 40 people were killed.