A health ministry official said at least 16 people had been injured in the clashes, some with birdshot wounds.
The protesters were marking the anniversary of deadly protests in 2011 against the military which took power between president Hosni Mubarak's overthrow and his now deposed successor Mohamed Morsi's election in June 2012.
Egypt is divided between supporters of Morsi and of the military that overthrew him, but yesterday's protesters accused both sides of betraying the goals of a 2011 uprising that ousted president Hosni Mubarak.
Police fired tear gas and shots at the protesters, who were hurling stones, before storming the square with armoured vehicles, scattering the few hundred protesters into side streets.
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Protesters covered their faces to protect themselves from the tear gas and health ministry official Ahmed al-Ansari told AFP 16 people were injured in the violence.
"I am here to retaliate for my friends killed in Mohamed Mahmud," said one protester, referring to 2011 clashes between protesters and police in a street off Tahrir Square.
The interior ministry said it had arrested 14 "rioters", including one in the possession of home made shotgun, and accused the protesters of trying to storm the Arab League's headquarters.
The November 2011 Mohamed Mahmud clashes were the first serious revolt faced by the military junta that had taken charge after Mubarak's resignation in February 2011.
The military handed power to Morsi in June 2012, after he won the country's first free election, but ousted him a year later following mass protests demanding his resignation.
Yesterday's clashes, however, took place between protesters who oppose both Morsi and the military appointed interim government.