Pro-Morsi demonstrators had gathered in the area around the university in response to protests demanding that the president step down.
The violence erupted late Tuesday before Morsi made a speech vowing to stay in office despite an army ultimatum, set to expire this afternoon, Egyptian news reports said.
The army said on Monday that the government had 48 hours to resolve the political unrest in the country or it would intervene.
Anti-government protests continued through the night in Tahrir Square in central Cairo.