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Activists called the protest to put pressure on President Mohamed Mursi to punish those responsible for killings and abuses during the rule of the generals who assumed power after Hosni Mubarak was toppled by an uprising in February 2011.
The skirmishes erupted at the scene of clashes last year in which 42 people were killed during protests against the military council that ran the country before Mursi was elected in June.
Nineteen people have been arrested in the latest round of violence, in which protesters hurling stones and petrol bombs at police guarding the ministry were repelled with teargas.
The public prosecutor has ordered an investigation, said the state news agency MENA, giving the figures for the arrested and injured.
Last year's street battles started when police pulled down the tents of protesters who had camped overnight in Tahrir Square - the heart of the uprising against Mubarak - after a demonstration against the generals.
That prompted thousands of protesters to return to the square and clashes erupted. The violence became known as the "Mohamed Mahmoud events" after the street in which they took place. The street is located off Tahrir Square.
In the latest protest, stones and empty bottles were hurled and 24 people were injured, including four policemen, by the early hours of Tuesday morning.
Some activists said the police had used force on Monday to try to stop protesters from taking down concrete barriers which have blocked off roads to the Interior Ministry since last year.
Television footage showed different groups of people present in the area from the previous evening.
The footage showed children and teenagers, some of them carrying school backpacks, taking part. Some were shown throwing rocks at buildings. One youth was pictured using a fire extinguisher to smash a window.
Protests, which have become frequent in Egypt since Mubarak's overthrow, often begin calmly before attracting what some democracy activists have described as delinquent youths looking for trouble.